{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1c42c80c",
   "metadata": {},
   "source": [
    "### Big n methods ###\n",
    "\n",
    "As you discussed in class, when the sample size is large we run into a couple of new problems. \n",
    "- 1. Just data exploration can become time consuming or difficult. It's hard to check assumptions when you can't even plot the data.\n",
    "- 2. p-values become essentially meaningless.\n",
    "\n",
    "What are we going to do?\n",
    "\n",
    "Let's start by looking at a big data set on housing pricing from King County (Seattle, WA). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f809d17b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: 'dplyr'\n",
      "\n",
      "\n",
      "The following objects are masked from 'package:stats':\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "\n",
      "The following objects are masked from 'package:base':\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'id'</li><li>'date'</li><li>'price'</li><li>'bedrooms'</li><li>'bathrooms'</li><li>'sqft_living'</li><li>'sqft_lot'</li><li>'floors'</li><li>'waterfront'</li><li>'view'</li><li>'condition'</li><li>'grade'</li><li>'sqft_above'</li><li>'sqft_basement'</li><li>'yr_built'</li><li>'yr_renovated'</li><li>'zipcode'</li><li>'lat'</li><li>'long'</li><li>'sqft_living15'</li><li>'sqft_lot15'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'id'\n",
       "\\item 'date'\n",
       "\\item 'price'\n",
       "\\item 'bedrooms'\n",
       "\\item 'bathrooms'\n",
       "\\item 'sqft\\_living'\n",
       "\\item 'sqft\\_lot'\n",
       "\\item 'floors'\n",
       "\\item 'waterfront'\n",
       "\\item 'view'\n",
       "\\item 'condition'\n",
       "\\item 'grade'\n",
       "\\item 'sqft\\_above'\n",
       "\\item 'sqft\\_basement'\n",
       "\\item 'yr\\_built'\n",
       "\\item 'yr\\_renovated'\n",
       "\\item 'zipcode'\n",
       "\\item 'lat'\n",
       "\\item 'long'\n",
       "\\item 'sqft\\_living15'\n",
       "\\item 'sqft\\_lot15'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'id'\n",
       "2. 'date'\n",
       "3. 'price'\n",
       "4. 'bedrooms'\n",
       "5. 'bathrooms'\n",
       "6. 'sqft_living'\n",
       "7. 'sqft_lot'\n",
       "8. 'floors'\n",
       "9. 'waterfront'\n",
       "10. 'view'\n",
       "11. 'condition'\n",
       "12. 'grade'\n",
       "13. 'sqft_above'\n",
       "14. 'sqft_basement'\n",
       "15. 'yr_built'\n",
       "16. 'yr_renovated'\n",
       "17. 'zipcode'\n",
       "18. 'lat'\n",
       "19. 'long'\n",
       "20. 'sqft_living15'\n",
       "21. 'sqft_lot15'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"id\"            \"date\"          \"price\"         \"bedrooms\"     \n",
       " [5] \"bathrooms\"     \"sqft_living\"   \"sqft_lot\"      \"floors\"       \n",
       " [9] \"waterfront\"    \"view\"          \"condition\"     \"grade\"        \n",
       "[13] \"sqft_above\"    \"sqft_basement\" \"yr_built\"      \"yr_renovated\" \n",
       "[17] \"zipcode\"       \"lat\"           \"long\"          \"sqft_living15\"\n",
       "[21] \"sqft_lot15\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 21</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>id</th><th scope=col>date</th><th scope=col>price</th><th scope=col>bedrooms</th><th scope=col>bathrooms</th><th scope=col>sqft_living</th><th scope=col>sqft_lot</th><th scope=col>floors</th><th scope=col>waterfront</th><th scope=col>view</th><th scope=col>...</th><th scope=col>grade</th><th scope=col>sqft_above</th><th scope=col>sqft_basement</th><th scope=col>yr_built</th><th scope=col>yr_renovated</th><th scope=col>zipcode</th><th scope=col>lat</th><th scope=col>long</th><th scope=col>sqft_living15</th><th scope=col>sqft_lot15</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>...</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>7129300520</td><td>20141013T000000</td><td> 221900</td><td>3</td><td>1.00</td><td>1180</td><td>  5650</td><td>1</td><td>0</td><td>0</td><td>...</td><td> 7</td><td>1180</td><td>   0</td><td>1955</td><td>   0</td><td>98178</td><td>47.5112</td><td>-122.257</td><td>1340</td><td>  5650</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>6414100192</td><td>20141209T000000</td><td> 538000</td><td>3</td><td>2.25</td><td>2570</td><td>  7242</td><td>2</td><td>0</td><td>0</td><td>...</td><td> 7</td><td>2170</td><td> 400</td><td>1951</td><td>1991</td><td>98125</td><td>47.7210</td><td>-122.319</td><td>1690</td><td>  7639</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>5631500400</td><td>20150225T000000</td><td> 180000</td><td>2</td><td>1.00</td><td> 770</td><td> 10000</td><td>1</td><td>0</td><td>0</td><td>...</td><td> 6</td><td> 770</td><td>   0</td><td>1933</td><td>   0</td><td>98028</td><td>47.7379</td><td>-122.233</td><td>2720</td><td>  8062</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>2487200875</td><td>20141209T000000</td><td> 604000</td><td>4</td><td>3.00</td><td>1960</td><td>  5000</td><td>1</td><td>0</td><td>0</td><td>...</td><td> 7</td><td>1050</td><td> 910</td><td>1965</td><td>   0</td><td>98136</td><td>47.5208</td><td>-122.393</td><td>1360</td><td>  5000</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1954400510</td><td>20150218T000000</td><td> 510000</td><td>3</td><td>2.00</td><td>1680</td><td>  8080</td><td>1</td><td>0</td><td>0</td><td>...</td><td> 8</td><td>1680</td><td>   0</td><td>1987</td><td>   0</td><td>98074</td><td>47.6168</td><td>-122.045</td><td>1800</td><td>  7503</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>7237550310</td><td>20140512T000000</td><td>1225000</td><td>4</td><td>4.50</td><td>5420</td><td>101930</td><td>1</td><td>0</td><td>0</td><td>...</td><td>11</td><td>3890</td><td>1530</td><td>2001</td><td>   0</td><td>98053</td><td>47.6561</td><td>-122.005</td><td>4760</td><td>101930</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 21\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & id & date & price & bedrooms & bathrooms & sqft\\_living & sqft\\_lot & floors & waterfront & view & ... & grade & sqft\\_above & sqft\\_basement & yr\\_built & yr\\_renovated & zipcode & lat & long & sqft\\_living15 & sqft\\_lot15\\\\\n",
       "  & <dbl> & <chr> & <dbl> & <int> & <dbl> & <int> & <int> & <dbl> & <int> & <int> & ... & <int> & <int> & <int> & <int> & <int> & <int> & <dbl> & <dbl> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t1 & 7129300520 & 20141013T000000 &  221900 & 3 & 1.00 & 1180 &   5650 & 1 & 0 & 0 & ... &  7 & 1180 &    0 & 1955 &    0 & 98178 & 47.5112 & -122.257 & 1340 &   5650\\\\\n",
       "\t2 & 6414100192 & 20141209T000000 &  538000 & 3 & 2.25 & 2570 &   7242 & 2 & 0 & 0 & ... &  7 & 2170 &  400 & 1951 & 1991 & 98125 & 47.7210 & -122.319 & 1690 &   7639\\\\\n",
       "\t3 & 5631500400 & 20150225T000000 &  180000 & 2 & 1.00 &  770 &  10000 & 1 & 0 & 0 & ... &  6 &  770 &    0 & 1933 &    0 & 98028 & 47.7379 & -122.233 & 2720 &   8062\\\\\n",
       "\t4 & 2487200875 & 20141209T000000 &  604000 & 4 & 3.00 & 1960 &   5000 & 1 & 0 & 0 & ... &  7 & 1050 &  910 & 1965 &    0 & 98136 & 47.5208 & -122.393 & 1360 &   5000\\\\\n",
       "\t5 & 1954400510 & 20150218T000000 &  510000 & 3 & 2.00 & 1680 &   8080 & 1 & 0 & 0 & ... &  8 & 1680 &    0 & 1987 &    0 & 98074 & 47.6168 & -122.045 & 1800 &   7503\\\\\n",
       "\t6 & 7237550310 & 20140512T000000 & 1225000 & 4 & 4.50 & 5420 & 101930 & 1 & 0 & 0 & ... & 11 & 3890 & 1530 & 2001 &    0 & 98053 & 47.6561 & -122.005 & 4760 & 101930\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 21\n",
       "\n",
       "| <!--/--> | id &lt;dbl&gt; | date &lt;chr&gt; | price &lt;dbl&gt; | bedrooms &lt;int&gt; | bathrooms &lt;dbl&gt; | sqft_living &lt;int&gt; | sqft_lot &lt;int&gt; | floors &lt;dbl&gt; | waterfront &lt;int&gt; | view &lt;int&gt; | ... ... | grade &lt;int&gt; | sqft_above &lt;int&gt; | sqft_basement &lt;int&gt; | yr_built &lt;int&gt; | yr_renovated &lt;int&gt; | zipcode &lt;int&gt; | lat &lt;dbl&gt; | long &lt;dbl&gt; | sqft_living15 &lt;int&gt; | sqft_lot15 &lt;int&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 7129300520 | 20141013T000000 |  221900 | 3 | 1.00 | 1180 |   5650 | 1 | 0 | 0 | ... |  7 | 1180 |    0 | 1955 |    0 | 98178 | 47.5112 | -122.257 | 1340 |   5650 |\n",
       "| 2 | 6414100192 | 20141209T000000 |  538000 | 3 | 2.25 | 2570 |   7242 | 2 | 0 | 0 | ... |  7 | 2170 |  400 | 1951 | 1991 | 98125 | 47.7210 | -122.319 | 1690 |   7639 |\n",
       "| 3 | 5631500400 | 20150225T000000 |  180000 | 2 | 1.00 |  770 |  10000 | 1 | 0 | 0 | ... |  6 |  770 |    0 | 1933 |    0 | 98028 | 47.7379 | -122.233 | 2720 |   8062 |\n",
       "| 4 | 2487200875 | 20141209T000000 |  604000 | 4 | 3.00 | 1960 |   5000 | 1 | 0 | 0 | ... |  7 | 1050 |  910 | 1965 |    0 | 98136 | 47.5208 | -122.393 | 1360 |   5000 |\n",
       "| 5 | 1954400510 | 20150218T000000 |  510000 | 3 | 2.00 | 1680 |   8080 | 1 | 0 | 0 | ... |  8 | 1680 |    0 | 1987 |    0 | 98074 | 47.6168 | -122.045 | 1800 |   7503 |\n",
       "| 6 | 7237550310 | 20140512T000000 | 1225000 | 4 | 4.50 | 5420 | 101930 | 1 | 0 | 0 | ... | 11 | 3890 | 1530 | 2001 |    0 | 98053 | 47.6561 | -122.005 | 4760 | 101930 |\n",
       "\n"
      ],
      "text/plain": [
       "  id         date            price   bedrooms bathrooms sqft_living sqft_lot\n",
       "1 7129300520 20141013T000000  221900 3        1.00      1180          5650  \n",
       "2 6414100192 20141209T000000  538000 3        2.25      2570          7242  \n",
       "3 5631500400 20150225T000000  180000 2        1.00       770         10000  \n",
       "4 2487200875 20141209T000000  604000 4        3.00      1960          5000  \n",
       "5 1954400510 20150218T000000  510000 3        2.00      1680          8080  \n",
       "6 7237550310 20140512T000000 1225000 4        4.50      5420        101930  \n",
       "  floors waterfront view ... grade sqft_above sqft_basement yr_built\n",
       "1 1      0          0    ...  7    1180          0          1955    \n",
       "2 2      0          0    ...  7    2170        400          1951    \n",
       "3 1      0          0    ...  6     770          0          1933    \n",
       "4 1      0          0    ...  7    1050        910          1965    \n",
       "5 1      0          0    ...  8    1680          0          1987    \n",
       "6 1      0          0    ... 11    3890       1530          2001    \n",
       "  yr_renovated zipcode lat     long     sqft_living15 sqft_lot15\n",
       "1    0         98178   47.5112 -122.257 1340            5650    \n",
       "2 1991         98125   47.7210 -122.319 1690            7639    \n",
       "3    0         98028   47.7379 -122.233 2720            8062    \n",
       "4    0         98136   47.5208 -122.393 1360            5000    \n",
       "5    0         98074   47.6168 -122.045 1800            7503    \n",
       "6    0         98053   47.6561 -122.005 4760          101930    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>21613</li><li>21</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 21613\n",
       "\\item 21\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 21613\n",
       "2. 21\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 21613    21"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's load the data\n",
    "library(dplyr)\n",
    "library(ggplot2)\n",
    "kc_orig<-read.csv(\"kc_house_data.csv\")\n",
    "kc<-kc_orig\n",
    "names(kc)\n",
    "head(kc)\n",
    "dim(kc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3683b8b3",
   "metadata": {},
   "source": [
    "We have 20000+ samples and 21 dimensions. I will limit the study to a few of the features here to keep things simple. Explore more of them at home.\n",
    "\n",
    "I start by eliminating indeces, dates and zipcodes. Note, these can be important predictors for house pricing (location and time of sale if there are trends in the data). In fact, since you have so much data you can indeed use the zipcode as a high-level categorical feature for example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "65231306",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'price'</li><li>'bedrooms'</li><li>'bathrooms'</li><li>'sqft_living'</li><li>'sqft_lot'</li><li>'floors'</li><li>'waterfront'</li><li>'view'</li><li>'condition'</li><li>'grade'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'price'\n",
       "\\item 'bedrooms'\n",
       "\\item 'bathrooms'\n",
       "\\item 'sqft\\_living'\n",
       "\\item 'sqft\\_lot'\n",
       "\\item 'floors'\n",
       "\\item 'waterfront'\n",
       "\\item 'view'\n",
       "\\item 'condition'\n",
       "\\item 'grade'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'price'\n",
       "2. 'bedrooms'\n",
       "3. 'bathrooms'\n",
       "4. 'sqft_living'\n",
       "5. 'sqft_lot'\n",
       "6. 'floors'\n",
       "7. 'waterfront'\n",
       "8. 'view'\n",
       "9. 'condition'\n",
       "10. 'grade'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"price\"       \"bedrooms\"    \"bathrooms\"   \"sqft_living\" \"sqft_lot\"   \n",
       " [6] \"floors\"      \"waterfront\"  \"view\"        \"condition\"   \"grade\"      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 10</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>price</th><th scope=col>bedrooms</th><th scope=col>bathrooms</th><th scope=col>sqft_living</th><th scope=col>sqft_lot</th><th scope=col>floors</th><th scope=col>waterfront</th><th scope=col>view</th><th scope=col>condition</th><th scope=col>grade</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>5.346157</td><td>3</td><td>1.00</td><td>1180</td><td>  5650</td><td>1</td><td>0</td><td>0</td><td>3</td><td> 7</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>5.730782</td><td>3</td><td>2.25</td><td>2570</td><td>  7242</td><td>2</td><td>0</td><td>0</td><td>3</td><td> 7</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>5.255273</td><td>2</td><td>1.00</td><td> 770</td><td> 10000</td><td>1</td><td>0</td><td>0</td><td>3</td><td> 6</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>5.781037</td><td>4</td><td>3.00</td><td>1960</td><td>  5000</td><td>1</td><td>0</td><td>0</td><td>5</td><td> 7</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>5.707570</td><td>3</td><td>2.00</td><td>1680</td><td>  8080</td><td>1</td><td>0</td><td>0</td><td>3</td><td> 8</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>6.088136</td><td>4</td><td>4.50</td><td>5420</td><td>101930</td><td>1</td><td>0</td><td>0</td><td>3</td><td>11</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 10\n",
       "\\begin{tabular}{r|llllllllll}\n",
       "  & price & bedrooms & bathrooms & sqft\\_living & sqft\\_lot & floors & waterfront & view & condition & grade\\\\\n",
       "  & <dbl> & <int> & <dbl> & <int> & <int> & <dbl> & <int> & <int> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t1 & 5.346157 & 3 & 1.00 & 1180 &   5650 & 1 & 0 & 0 & 3 &  7\\\\\n",
       "\t2 & 5.730782 & 3 & 2.25 & 2570 &   7242 & 2 & 0 & 0 & 3 &  7\\\\\n",
       "\t3 & 5.255273 & 2 & 1.00 &  770 &  10000 & 1 & 0 & 0 & 3 &  6\\\\\n",
       "\t4 & 5.781037 & 4 & 3.00 & 1960 &   5000 & 1 & 0 & 0 & 5 &  7\\\\\n",
       "\t5 & 5.707570 & 3 & 2.00 & 1680 &   8080 & 1 & 0 & 0 & 3 &  8\\\\\n",
       "\t6 & 6.088136 & 4 & 4.50 & 5420 & 101930 & 1 & 0 & 0 & 3 & 11\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 10\n",
       "\n",
       "| <!--/--> | price &lt;dbl&gt; | bedrooms &lt;int&gt; | bathrooms &lt;dbl&gt; | sqft_living &lt;int&gt; | sqft_lot &lt;int&gt; | floors &lt;dbl&gt; | waterfront &lt;int&gt; | view &lt;int&gt; | condition &lt;int&gt; | grade &lt;int&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 5.346157 | 3 | 1.00 | 1180 |   5650 | 1 | 0 | 0 | 3 |  7 |\n",
       "| 2 | 5.730782 | 3 | 2.25 | 2570 |   7242 | 2 | 0 | 0 | 3 |  7 |\n",
       "| 3 | 5.255273 | 2 | 1.00 |  770 |  10000 | 1 | 0 | 0 | 3 |  6 |\n",
       "| 4 | 5.781037 | 4 | 3.00 | 1960 |   5000 | 1 | 0 | 0 | 5 |  7 |\n",
       "| 5 | 5.707570 | 3 | 2.00 | 1680 |   8080 | 1 | 0 | 0 | 3 |  8 |\n",
       "| 6 | 6.088136 | 4 | 4.50 | 5420 | 101930 | 1 | 0 | 0 | 3 | 11 |\n",
       "\n"
      ],
      "text/plain": [
       "  price    bedrooms bathrooms sqft_living sqft_lot floors waterfront view\n",
       "1 5.346157 3        1.00      1180          5650   1      0          0   \n",
       "2 5.730782 3        2.25      2570          7242   2      0          0   \n",
       "3 5.255273 2        1.00       770         10000   1      0          0   \n",
       "4 5.781037 4        3.00      1960          5000   1      0          0   \n",
       "5 5.707570 3        2.00      1680          8080   1      0          0   \n",
       "6 6.088136 4        4.50      5420        101930   1      0          0   \n",
       "  condition grade\n",
       "1 3          7   \n",
       "2 3          7   \n",
       "3 3          6   \n",
       "4 5          7   \n",
       "5 3          8   \n",
       "6 3         11   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kc2<-kc[,-c(1,2,13:21)]\n",
    "kc2$price<-log10(kc$price)               # basic transformations of the data\n",
    "#\n",
    "names(kc2)\n",
    "head(kc2)\n",
    "# Note we have categorical/ordinal variables here for grade and condition\n",
    "# These may not always be well suited to be treated as numerical in which case you may want to \n",
    "# encode these as dummy variables. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ea59093",
   "metadata": {},
   "source": [
    "Let's run a simple visual exploration of the data, scatter plots. You will notice this takes a while because you have a lot of data. Also, the scatter plots are really dense which make them difficult to explore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e56ebcce",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'GGally' was built under R version 4.1.3\"\n",
      "Registered S3 method overwritten by 'GGally':\n",
      "  method from   \n",
      "  +.gg   ggplot2\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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uP/d4NE3EbaACTqeaRgjmgL3c5l0iJ9pFA5LgGM9N/sIJmPI+EwDG6QVA4gJNdI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\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(GGally)\n",
    "ggpairs(data=kc2,\n",
    "        axisLabels=\"show\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "871fd39d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MEdDl45d2CAtFlQo4ognXr6O7hDe7Sy1wRIhAASrymHpNrLLCbeO0gDQGIFkAQS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\nYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggpairs(data=kc2,columns=c(2,3,4,1)) #  looks like we should try a transformation on sqft_living\n",
    "                                    #  and a huge outlier in bedrooms (30 bedrooms?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3856969",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fvu7QBSNXH3jzGSSOv2ndslg7T+AaRjcffPAySGs3bi18cAUpS4+2dxaRcZUuOA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\nCYIIBJAgiEAACYIIBJAgiED/B/zjx7QZ72f6AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kc3 <- kc2\n",
    "kc3 <- kc2[kc2$bedroom<20,]\n",
    "kc3$sqft_living <- sqrt(kc3$sqft_living)\n",
    "ggpairs(data=kc3,columns=c(2,3,4,1)) #  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "88855a3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FE/kzsgIX7fOmGQ2JsiAaRjBJAYP5P7AJCGW0Lkb9MHkI4RQGL8TO4sSP5ZuuVZ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\nPygCSL63BqT4qalNIJ1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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dpbCJBCX31JkKxO88olkGLLewSpaQFAOlf6DlmBSje2778NkNIPAp1/YHLUFEE6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\nSaDSb0KQICBpf66dyFeo6wApdFb0XghSgCSCtKJh7pQ/abXYv1a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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggpairs(data=kc3,columns=c(5,6,7,1)) #  \n",
    "ggpairs(data=kc3,columns=c(8,9,10,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c1c6b7a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "kc4 <- kc3\n",
    "kc4$sqft_lot <- sqrt(kc3$sqft_lot) # compress the size of the lot scale\n",
    "kc4$view[kc4$view>1] <- 1          # for simplicity use view as binary variable (has view or not)\n",
    "# other ordingal look quite good.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bafe60fe",
   "metadata": {},
   "source": [
    "After some (very simple) data exploration steps we are ready to run a linear model fit. \n",
    "\n",
    "With 20000+ observations all coefficient estimates are highly significant! Compare this to the patterns you see in the scatter plots above...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0e14283e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ ., data = kc4)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.53332 -0.10273  0.00485  0.09811  0.60416 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  4.530e+00  9.710e-03 466.569  < 2e-16 ***\n",
       "bedrooms    -1.257e-02  1.459e-03  -8.613  < 2e-16 ***\n",
       "bathrooms   -4.668e-03  2.197e-03  -2.125  0.03361 *  \n",
       "sqft_living  9.551e-03  2.233e-04  42.770  < 2e-16 ***\n",
       "sqft_lot    -1.630e-04  1.519e-05 -10.727  < 2e-16 ***\n",
       "floors       6.576e-03  2.280e-03   2.884  0.00393 ** \n",
       "waterfront   1.958e-01  1.189e-02  16.466  < 2e-16 ***\n",
       "view         8.894e-02  3.598e-03  24.718  < 2e-16 ***\n",
       "condition    4.171e-02  1.591e-03  26.216  < 2e-16 ***\n",
       "grade        8.056e-02  1.410e-03  57.139  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1455 on 21602 degrees of freedom\n",
       "Multiple R-squared:  0.5953,\tAdjusted R-squared:  0.5951 \n",
       "F-statistic:  3531 on 9 and 21602 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mm <- lm(price~., data=kc4)\n",
    "summary(mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f15afc89",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n"
     ]
    },
    {
     "data": {
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VLeW82nKRkk2Yha1NbX708E0j5C6gtr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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4BkjyLm3LLsgrBfNUjn+uW7aT7O9bvj0SWPuKv7ruwBki1KeypobyD9q5+7z4/6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\nCCBBUAQBJAiKIIAEQRH0//FL43jpJFyOAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "custom_function = function(data, mapping, method1 = \"loess\", method2= \"lm\", ...){\n",
    "      p = ggplot(data = data, mapping = mapping) + \n",
    "      geom_point() + \n",
    "      geom_smooth(method=method1, color=\"blue\")+\n",
    "      geom_smooth(method=method2, color=\"red\")\n",
    "      p\n",
    "    }\n",
    "#\n",
    "options(warn=-1)\n",
    "ggpairs(data=kc4[sample(seq(1,dim(kc4)[1]),5000),c(2,3,4,5,1)],\n",
    "        axisLabels=\"show\",\n",
    "        lower = list(continuous = custom_function))\n",
    "ggpairs(data=kc4[sample(seq(1,dim(kc4)[1]),5000),c(6,7,8,9,10,1)],\n",
    "        axisLabels=\"show\",\n",
    "        lower = list(continuous = custom_function))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3798c350",
   "metadata": {},
   "source": [
    "There is some indiciation that you might want to turn e.g. condition into a categorical/ordinal and for low grade the linear trend appears broken. Note also that the lot size migth be better to truncate. \n",
    "\n",
    "Explore this at home but for now let's move on to explore the big n problems."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c81f174f",
   "metadata": {},
   "source": [
    "First - random projections were introduced in class. If the true data matrix is low rank you can estimate its low rank summary quite fast via random projections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "539fadbc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05 sec elapsed\n",
      "0.21 sec elapsed\n"
     ]
    }
   ],
   "source": [
    "# Note, here I just to compare run times over dimensions and not the approximations \n",
    "# Try this on low rank matrices at home\n",
    "library(tictoc)\n",
    "library(rsvd)\n",
    "#\n",
    "X<-matrix(rnorm(1000000),10000,100)\n",
    "tic()\n",
    "s <- rsvd(X,k=10,p=2,q=1) # askking for a higher rank k means you get closer to svd computation...\n",
    "toc()\n",
    "\n",
    "tic()\n",
    "s <- svd(X)\n",
    "toc()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1b46b259",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 sec elapsed\n",
      "0.05 sec elapsed\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(warn=0)\n",
    "library(rsvd) # a package for randomized projections.\n",
    "###\n",
    "standardize <- function(x) {x <- (x-mean(x))/sd(x)}\n",
    "kc5 <- kc4\n",
    "kc5[,-1] <- as.matrix(apply(kc4[,-1],2,standardize))\n",
    "#\n",
    "tic()\n",
    "ss <- svd(kc5[,-1]) # \n",
    "toc()\n",
    "#\n",
    "tic()\n",
    "ssr <- rsvd(as.matrix(kc5[,-1]),p=5,q=1) # \n",
    "toc()\n",
    "#\n",
    "plot(ss$u[,1],ssr$u[,1],xlab=\"PC1\",ylab=\"rPC1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b38e7159",
   "metadata": {},
   "source": [
    "For this size data we don't have a big problem running svd as is. We will push the limit a bit more further down.\n",
    "\n",
    "In class we talked about *leveraging*. Here, we reduce the size of the data based on their leverage (diagonal entries from the hat-matrix) to retain those observations that most drive the fit of the model.\n",
    "\n",
    "As we saw from class, we don't need to fit the data to get the leverages. We only need to run SVD (or randomized SVD) on the data matrix!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "81fb7289",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QRYE8n5baKLVIZwrc95A91/fvVdhh9a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\nPGY9WvPUw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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Nbr of high leverage observations =  1667\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Leveraging\n",
    "library(rsvd)\n",
    "ss<-rsvd(as.matrix(kc5[,-1])) # excluding the response variable\n",
    "lev<-apply(ss$u^2,1,sum) # leverage from the SVD of X\n",
    "plot(lev,type=\"h\",xlab=\"observations\",ylab=\"leverage\")\n",
    "abline(h=2*(dim(kc5)[2]-1)/(dim(kc5)[1]),col=\"darkorange\",lty=2,lwd=2)\n",
    "mm0<-lm(price~., data=kc5)\n",
    "hat<-hatvalues(mm0) # from the regression fit\n",
    "plot(hat,type=\"h\",xlab=\"observations\",ylab=\"leverage\")\n",
    "abline(h=2*(dim(kc5)[2]-1)/(dim(kc5)[1]),col=\"darkorange\",lty=2,lwd=2)\n",
    "###\n",
    "print(paste(\"Nbr of high leverage observations = \", length(lev[lev>2*(dim(kc5)[2]-1)/(dim(kc5)[1])])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8ff80ea",
   "metadata": {},
   "source": [
    "We can now use leverage (without computing the fit) to reduce the data set to a set of informative observations with some effectice sample size that's more reasonable to analyze/explore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f8f77474",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "515"
      ],
      "text/latex": [
       "515"
      ],
      "text/markdown": [
       "515"
      ],
      "text/plain": [
       "[1] 515"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UKCACFBgJAgQEgQICQIEBIECAkChAQB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\nBAgJAoQEAUKCACFBgJAgQEgQ8D/XIc0tXaylHgAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Histogram of lev\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1012)\n",
    "hist(lev,500)\n",
    "# sampling 500 observations with different probabilities given by leverage\n",
    "# so we oversample influential observations\n",
    "probs<-lev*500/sum(lev) # effective sample size 500\n",
    "probs[probs>1]<-1\n",
    "pp<-rbinom(dim(kc5)[1],prob=probs,size=1)\n",
    "sum(pp) # actual sample size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "344c2662",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using formula 'y ~ x'\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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Y24+uoAkt20O8PpQDjUUpp29m7dbH2+aPgCIEXeBBjYBfyqfRWeyNriGrBcfW0P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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/t+4ug0vy1s39DgXYbZRWWF8mCGdhAZAlI3sTVWs0Xar2O4nuyZOrjccdZOQMLF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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "custom_function = function(data, mapping, method1 = \"loess\", method2= \"lm\", ...){\n",
    "      p = ggplot(data = data, mapping = mapping) + \n",
    "      geom_point() + \n",
    "      #geom_smooth(method=method1, color=\"blue\")+\n",
    "      geom_smooth(method=method2, color=\"red\")\n",
    "      p\n",
    "    }\n",
    "#\n",
    "set.seed(2021)\n",
    "options(warn=-1)\n",
    "kc6a <- as.data.frame(kc5[sample(seq(1,dim(kc5)[1]),500),])\n",
    "names(kc6a)<-names(kc5)\n",
    "ggpairs(data=kc6a[,c(2,3,4,5,1)], # random samples\n",
    "        axisLabels=\"show\",\n",
    "        lower = list(continuous = custom_function))\n",
    "kc6b <- as.data.frame(kc5[pp==1,])\n",
    "names(kc6b)<-names(kc5)\n",
    "ggpairs(data=kc6b[,c(2,3,4,5,1)],                             # high leverage samples\n",
    "        axisLabels=\"show\",\n",
    "        lower = list(continuous = custom_function))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51ab8a9e",
   "metadata": {},
   "source": [
    "I run regression on the reduced sample data. You get a better fit when you used leverage sampling by design - you asked for the observations in the extremes of x which of course increases the R-squared. \n",
    "\n",
    "Leverage can be used to subsample the data for fast model exploration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8be0007e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ ., data = kc6a)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.41494 -0.10224  0.00609  0.08973  0.40157 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  5.678273   0.006521 870.715  < 2e-16 ***\n",
       "bedrooms    -0.004323   0.008272  -0.523  0.60146    \n",
       "bathrooms   -0.001420   0.010843  -0.131  0.89589    \n",
       "sqft_living  0.079287   0.013336   5.945 5.25e-09 ***\n",
       "sqft_lot    -0.021486   0.007645  -2.811  0.00514 ** \n",
       "floors      -0.009739   0.007841  -1.242  0.21481    \n",
       "waterfront   0.024909   0.005471   4.553 6.69e-06 ***\n",
       "view         0.020775   0.006782   3.063  0.00231 ** \n",
       "condition    0.018356   0.006406   2.865  0.00434 ** \n",
       "grade        0.093523   0.011202   8.349 7.11e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.144 on 490 degrees of freedom\n",
       "Multiple R-squared:  0.541,\tAdjusted R-squared:  0.5325 \n",
       "F-statistic: 64.16 on 9 and 490 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ ., data = kc6b)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.48596 -0.09851  0.00633  0.09034  0.44992 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  5.681164   0.007839 724.689  < 2e-16 ***\n",
       "bedrooms     0.002282   0.006541   0.349    0.727    \n",
       "bathrooms   -0.004929   0.009857  -0.500    0.617    \n",
       "sqft_living  0.079341   0.012336   6.431 2.93e-10 ***\n",
       "sqft_lot    -0.003748   0.003253  -1.152    0.250    \n",
       "floors       0.001586   0.007578   0.209    0.834    \n",
       "waterfront   0.017040   0.002270   7.506 2.77e-13 ***\n",
       "view         0.024881   0.005513   4.513 7.95e-06 ***\n",
       "condition    0.026815   0.006193   4.330 1.80e-05 ***\n",
       "grade        0.096158   0.009621   9.994  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1546 on 505 degrees of freedom\n",
       "Multiple R-squared:  0.7132,\tAdjusted R-squared:  0.7081 \n",
       "F-statistic: 139.5 on 9 and 505 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mm6a <- lm(price~., data=kc6a)\n",
    "summary(mm6a)\n",
    "mm6b <- lm(price~., data=kc6b)\n",
    "summary(mm6b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f45a3b47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ sqft_living + bedrooms + condition + grade, \n",
       "    data = kc7)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.5113 -0.1056  0.0023  0.0996  0.6049 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error  t value Pr(>|t|)    \n",
       "(Intercept)  5.6663182  0.0003345 16940.33   <2e-16 ***\n",
       "sqft_living  0.0952904  0.0006295   151.38   <2e-16 ***\n",
       "bedrooms    -0.0158638  0.0004393   -36.11   <2e-16 ***\n",
       "condition    0.0289979  0.0003389    85.55   <2e-16 ***\n",
       "grade        0.0990499  0.0005349   185.19   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1496 on 199995 degrees of freedom\n",
       "Multiple R-squared:  0.5752,\tAdjusted R-squared:  0.5751 \n",
       "F-statistic: 6.769e+04 on 4 and 199995 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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eM6MzlIJOm93sBp9jsb2L1DMcukVtKdQaIc1W6rpiYHaftK46z66BjjfS0ehxtN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\nG9rJNrXXg6biEWtm/CpSyVC1NBDbT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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ sqft_living + bedrooms + condition + grade, \n",
       "    data = kc7, subset = seq(1, dim(kc7)[1])[pp == 1])\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.51955 -0.12065 -0.00467  0.10945  0.54500 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error  t value Pr(>|t|)    \n",
       "(Intercept)  5.708633   0.004150 1375.476  < 2e-16 ***\n",
       "sqft_living  0.110473   0.005579   19.802  < 2e-16 ***\n",
       "bedrooms    -0.017127   0.003883   -4.411 1.08e-05 ***\n",
       "condition    0.026572   0.003380    7.862 6.19e-15 ***\n",
       "grade        0.094871   0.004902   19.354  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.173 on 1967 degrees of freedom\n",
       "Multiple R-squared:  0.6561,\tAdjusted R-squared:  0.6554 \n",
       "F-statistic: 938.1 on 4 and 1967 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EAas1iYpCOXM47/FTnqCBIkL/aWuF6b+iriDZE1ibipOEApNxANHpkaNoFRnxKQ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\nGVQXulOAAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ sqft_living + bedrooms + condition + grade, \n",
       "    data = kc7, subset = sample(seq(1, dim(kc7)[1]), sum(pp)))\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.43114 -0.10917 -0.00204  0.10181  0.45160 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error  t value Pr(>|t|)    \n",
       "(Intercept)  5.663491   0.003389 1670.935  < 2e-16 ***\n",
       "sqft_living  0.104983   0.006420   16.352  < 2e-16 ***\n",
       "bedrooms    -0.015905   0.004630   -3.435 0.000604 ***\n",
       "condition    0.029208   0.003379    8.644  < 2e-16 ***\n",
       "grade        0.094079   0.005525   17.029  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1504 on 1967 degrees of freedom\n",
       "Multiple R-squared:  0.5892,\tAdjusted R-squared:  0.5884 \n",
       "F-statistic: 705.3 on 4 and 1967 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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d2ueTmaEyTkxkO4VPs4SVgkNEgehhKK9N5tT0m6sKcag8mS51xdqm5VAdjD6gyQ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",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#####################################\n",
    "# run again but on 10 times as much data... which I artificially generate by oversampling just for illustration \n",
    "kc7<-kc5[sample(seq(1,dim(kc5)[1]),200000,replace=T),]\n",
    "#\n",
    "ss<-rsvd(as.matrix(kc7[,-1])) # excluding the response variable\n",
    "lev<-apply(ss$u^2,1,sum)\n",
    "probs<-lev*2000/sum(lev) # effective size 2000\n",
    "probs[probs>1]<-1 \n",
    "pp<-rbinom(dim(kc7)[1],prob=probs,size=1)\n",
    "#########\n",
    "mm1<-lm(price~sqft_living+bedrooms+condition+grade,data=kc7)\n",
    "par(mfrow=c(2,2))\n",
    "plot(mm1) # takes forever....\n",
    "summary(mm1)\n",
    "###\n",
    "# Leverage results\n",
    "mm2<-lm(price~sqft_living+bedrooms+condition+grade,\n",
    "       data=kc7,subset=seq(1,dim(kc7)[1])[pp==1])\n",
    "par(mfrow=c(2,2))\n",
    "plot(mm2)\n",
    "summary(mm2)\n",
    "#\n",
    "mm3<-lm(price~sqft_living+bedrooms+condition+grade,\n",
    "       data=kc7,subset=sample(seq(1,dim(kc7)[1]),sum(pp)))\n",
    "par(mfrow=c(2,2))\n",
    "plot(mm3)\n",
    "summary(mm3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e1ab6c5",
   "metadata": {},
   "source": [
    "Leverage was a way to subsample the data for exploration and modeling. Still, if you subsample a large amount of data we have a difficult time interpreting the p-values.\n",
    "\n",
    "How about we focus on the effect size or explained variance instead.\n",
    "\n",
    "Effect size is just looking at coefficient estimate magnitudes (easier if you standardize the data where appropriate - perhaps not for binary or categorical....).\n",
    "\n",
    "R-squared is another way of looking at the \"usefulness\" of the model. However, if we want to translate this to the coefficient we have to think about R-squared per feature.\n",
    "\n",
    "The package 'relaimpo' in R and 'https://pingouin-stats.org/generated/pingouin.linear_regression.html' for python has several metrics to do this. The 'relaimpo' paper: https://www.jstatsoft.org/article/view/v017i01\n",
    "\n",
    "- *first*: how much can each predictor explain about the response on its own?\n",
    "- *last*: by how much does the R-squared increase if you add the predictor after all the others are in the model?\n",
    "- *betasq*: the usual effect size as measured by the squared coefficient value, but standardized to account for the feature and response variances\n",
    "- *lmg*: the R-squared averaged out over the order in which the feature enters the model - this requires multiple fits with permutations.\n",
    "- *pwmd*: improved version of *lmg*\n",
    "- *pratt, genizi*: takes marginal correlation and feature correlation into account in the standarized coefficients\n",
    "- *car*: correlation adjusted importance, also takes feature correlation into account.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "452df18f",
   "metadata": {},
   "outputs": [],
   "source": [
    "library(relaimpo)\n",
    "library(rsvd)\n",
    "library(irlba)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8c481e22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Response variable: price \n",
       "Total response variance: 0.05232176 \n",
       "Analysis based on 21612 observations \n",
       "\n",
       "9 Regressors: \n",
       "bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade \n",
       "Proportion of variance explained by model: 59.53%\n",
       "Metrics are not normalized (rela=FALSE). \n",
       "\n",
       "Relative importance metrics: \n",
       "\n",
       "                    lmg         last       first       betasq\n",
       "bedrooms    0.031384699 1.389903e-03 0.123204834 0.0024882349\n",
       "bathrooms   0.081633296 8.458805e-05 0.303405872 0.0002469845\n",
       "sqft_living 0.182879727 3.427158e-02 0.480772201 0.1586909960\n",
       "sqft_lot    0.005748653 2.155801e-03 0.018850892 0.0024589528\n",
       "floors      0.024436274 1.558224e-04 0.096467800 0.0002410097\n",
       "waterfront  0.012730995 5.079664e-03 0.030481758 0.0054864076\n",
       "view        0.040575965 1.144690e-02 0.109389437 0.0133990840\n",
       "condition   0.010477420 1.287640e-02 0.001559798 0.0140755518\n",
       "grade       0.205424730 6.116636e-02 0.495138874 0.1714098788\n",
       "\n",
       "Average coefficients for different model sizes: \n",
       "\n",
       "                     1X        2Xs        3Xs         4Xs          5Xs\n",
       "bedrooms    0.080288814 0.04958885 0.02754854 0.012300982  0.002175660\n",
       "bathrooms   0.125994956 0.09686541 0.07178574 0.050680106  0.033381985\n",
       "sqft_living 0.158602798 0.14908436 0.13991322 0.131079860  0.122568315\n",
       "sqft_lot    0.031405602 0.01945716 0.01041278 0.003627811 -0.001432672\n",
       "floors      0.071044810 0.04672348 0.03006019 0.019067076  0.012126801\n",
       "waterfront  0.039935689 0.03285172 0.02800740 0.024647124  0.022239915\n",
       "view        0.075653472 0.06182347 0.05158759 0.044066043  0.038512701\n",
       "condition   0.009033903 0.01688466 0.02152424 0.024148053  0.025570955\n",
       "grade       0.160955078 0.14809749 0.13693899 0.127307665  0.119002839\n",
       "                     6Xs          7Xs          8Xs          9Xs\n",
       "bedrooms    -0.004247534 -0.008117248 -0.010306073 -0.011410032\n",
       "bathrooms    0.019644903  0.009155046  0.001544726 -0.003594810\n",
       "sqft_living  0.114353855  0.106403023  0.098674624  0.091120756\n",
       "sqft_lot    -0.005189930 -0.007959447 -0.009963021 -0.011342695\n",
       "floors       0.007957221  0.005575567  0.004266193  0.003551063\n",
       "waterfront   0.020441166  0.019038622  0.017901159  0.016942801\n",
       "view         0.034336926  0.031107905  0.028542668  0.026477607\n",
       "condition    0.026326778  0.026740572  0.026986970  0.027137753\n",
       "grade        0.111806944  0.105498164  0.099862179  0.094701988"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#help(calc.relimp) # this takes a while to run.... especially for many predictors\n",
    "mm1<-lm(price~.,data=kc5)\n",
    "calc.relimp(mm1, type = c(\"lmg\",\"last\", \"first\", \"betasq\") )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f76347ea",
   "metadata": {},
   "source": [
    "You can use bootstrap to assess stability of the feature importance meaures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "94bfa5b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Response variable: price \n",
       "Total response variance: 0.05232176 \n",
       "Analysis based on 21612 observations \n",
       "\n",
       "9 Regressors: \n",
       "bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade \n",
       "Proportion of variance explained by model: 59.53%\n",
       "Metrics are normalized to sum to 100% (rela=TRUE). \n",
       "\n",
       "Relative importance metrics: \n",
       "\n",
       "                    lmg         last        first\n",
       "bedrooms    0.052721542 0.0108056834 0.0742523674\n",
       "bathrooms   0.137131574 0.0006576228 0.1828548720\n",
       "sqft_living 0.307210245 0.2664415135 0.2897489716\n",
       "sqft_lot    0.009656867 0.0167600911 0.0113609448\n",
       "floors      0.041049239 0.0012114284 0.0581386485\n",
       "waterfront  0.021386143 0.0394914251 0.0183705673\n",
       "view        0.068161477 0.0889929612 0.0659261845\n",
       "condition   0.017600478 0.1001065207 0.0009400501\n",
       "grade       0.345082435 0.4755327538 0.2984073939\n",
       "\n",
       "Average coefficients for different model sizes: \n",
       "\n",
       "                     1X        2Xs        3Xs         4Xs          5Xs\n",
       "bedrooms    0.080288814 0.04958885 0.02754854 0.012300982  0.002175660\n",
       "bathrooms   0.125994956 0.09686541 0.07178574 0.050680106  0.033381985\n",
       "sqft_living 0.158602798 0.14908436 0.13991322 0.131079860  0.122568315\n",
       "sqft_lot    0.031405602 0.01945716 0.01041278 0.003627811 -0.001432672\n",
       "floors      0.071044810 0.04672348 0.03006019 0.019067076  0.012126801\n",
       "waterfront  0.039935689 0.03285172 0.02800740 0.024647124  0.022239915\n",
       "view        0.075653472 0.06182347 0.05158759 0.044066043  0.038512701\n",
       "condition   0.009033903 0.01688466 0.02152424 0.024148053  0.025570955\n",
       "grade       0.160955078 0.14809749 0.13693899 0.127307665  0.119002839\n",
       "                     6Xs          7Xs          8Xs          9Xs\n",
       "bedrooms    -0.004247534 -0.008117248 -0.010306073 -0.011410032\n",
       "bathrooms    0.019644903  0.009155046  0.001544726 -0.003594810\n",
       "sqft_living  0.114353855  0.106403023  0.098674624  0.091120756\n",
       "sqft_lot    -0.005189930 -0.007959447 -0.009963021 -0.011342695\n",
       "floors       0.007957221  0.005575567  0.004266193  0.003551063\n",
       "waterfront   0.020441166  0.019038622  0.017901159  0.016942801\n",
       "view         0.034336926  0.031107905  0.028542668  0.026477607\n",
       "condition    0.026326778  0.026740572  0.026986970  0.027137753\n",
       "grade        0.111806944  0.105498164  0.099862179  0.094701988\n",
       "\n",
       " \n",
       " Confidence interval information ( 50 bootstrap replicates, bty= perc ): \n",
       "Relative Contributions with confidence intervals: \n",
       " \n",
       "                                       Lower  Upper\n",
       "                  percentage 0.95      0.95   0.95  \n",
       "bedrooms.lmg      0.0527     ____E____ 0.0488 0.0562\n",
       "bathrooms.lmg     0.1371     __C______ 0.1320 0.1426\n",
       "sqft_living.lmg   0.3072     _B_______ 0.3018 0.3123\n",
       "sqft_lot.lmg      0.0097     ________I 0.0083 0.0110\n",
       "floors.lmg        0.0410     _____F___ 0.0388 0.0437\n",
       "waterfront.lmg    0.0214     ______GH_ 0.0177 0.0259\n",
       "view.lmg          0.0682     ___D_____ 0.0619 0.0741\n",
       "condition.lmg     0.0176     ______GH_ 0.0150 0.0201\n",
       "grade.lmg         0.3451     A________ 0.3385 0.3521\n",
       "                                                    \n",
       "bedrooms.last     0.0108     _____FG__ 0.0063 0.0208\n",
       "bathrooms.last    0.0007     _______HI 0.0000 0.0021\n",
       "sqft_living.last  0.2664     _B_______ 0.2513 0.2898\n",
       "sqft_lot.last     0.0168     _____FG__ 0.0123 0.0233\n",
       "floors.last       0.0012     _______HI 0.0003 0.0035\n",
       "waterfront.last   0.0395     ____E____ 0.0285 0.0487\n",
       "view.last         0.0890     __CD_____ 0.0724 0.1065\n",
       "condition.last    0.1001     __CD_____ 0.0868 0.1115\n",
       "grade.last        0.4755     A________ 0.4524 0.4976\n",
       "                                                    \n",
       "bedrooms.first    0.0743     ___D_____ 0.0676 0.0789\n",
       "bathrooms.first   0.1829     __C______ 0.1787 0.1873\n",
       "sqft_living.first 0.2897     _B_______ 0.2860 0.2930\n",
       "sqft_lot.first    0.0114     _______H_ 0.0091 0.0135\n",
       "floors.first      0.0581     _____F___ 0.0548 0.0616\n",
       "waterfront.first  0.0184     ______G__ 0.0150 0.0230\n",
       "view.first        0.0659     ____E____ 0.0612 0.0701\n",
       "condition.first   0.0009     ________I 0.0005 0.0017\n",
       "grade.first       0.2984     A________ 0.2937 0.3026\n",
       "\n",
       "Letters indicate the ranks covered by bootstrap CIs. \n",
       "(Rank bootstrap confidence intervals always obtained by percentile method) \n",
       "CAUTION: Bootstrap confidence intervals can be somewhat liberal. \n",
       "\n",
       " \n",
       " Differences between Relative Contributions: \n",
       " \n",
       "                                             Lower   Upper\n",
       "                             difference 0.95 0.95    0.95   \n",
       "bedrooms-bathrooms.lmg       -0.0844     *   -0.0900 -0.0811\n",
       "bedrooms-sqft_living.lmg     -0.2545     *   -0.2611 -0.2467\n",
       "bedrooms-sqft_lot.lmg         0.0431     *    0.0387  0.0478\n",
       "bedrooms-floors.lmg           0.0117     *    0.0070  0.0151\n",
       "bedrooms-waterfront.lmg       0.0313     *    0.0250  0.0365\n",
       "bedrooms-view.lmg            -0.0154     *   -0.0220 -0.0097\n",
       "bedrooms-condition.lmg        0.0351     *    0.0309  0.0401\n",
       "bedrooms-grade.lmg           -0.2924     *   -0.3014 -0.2825\n",
       "bathrooms-sqft_living.lmg    -0.1701     *   -0.1753 -0.1604\n",
       "bathrooms-sqft_lot.lmg        0.1275     *    0.1218  0.1335\n",
       "bathrooms-floors.lmg          0.0961     *    0.0902  0.1022\n",
       "bathrooms-waterfront.lmg      0.1157     *    0.1103  0.1224\n",
       "bathrooms-view.lmg            0.0690     *    0.0604  0.0764\n",
       "bathrooms-condition.lmg       0.1195     *    0.1143  0.1257\n",
       "bathrooms-grade.lmg          -0.2080     *   -0.2197 -0.1987\n",
       "sqft_living-sqft_lot.lmg      0.2976     *    0.2919  0.3028\n",
       "sqft_living-floors.lmg        0.2662     *    0.2589  0.2721\n",
       "sqft_living-waterfront.lmg    0.2858     *    0.2785  0.2926\n",
       "sqft_living-view.lmg          0.2390     *    0.2317  0.2478\n",
       "sqft_living-condition.lmg     0.2896     *    0.2826  0.2963\n",
       "sqft_living-grade.lmg        -0.0379     *   -0.0465 -0.0276\n",
       "sqft_lot-floors.lmg          -0.0314     *   -0.0351 -0.0287\n",
       "sqft_lot-waterfront.lmg      -0.0117     *   -0.0162 -0.0080\n",
       "sqft_lot-view.lmg            -0.0585     *   -0.0648 -0.0515\n",
       "sqft_lot-condition.lmg       -0.0079     *   -0.0110 -0.0055\n",
       "sqft_lot-grade.lmg           -0.3354     *   -0.3417 -0.3293\n",
       "floors-waterfront.lmg         0.0197     *    0.0148  0.0247\n",
       "floors-view.lmg              -0.0271     *   -0.0344 -0.0193\n",
       "floors-condition.lmg          0.0234     *    0.0204  0.0274\n",
       "floors-grade.lmg             -0.3040     *   -0.3100 -0.2962\n",
       "waterfront-view.lmg          -0.0468     *   -0.0542 -0.0401\n",
       "waterfront-condition.lmg      0.0038         -0.0015  0.0099\n",
       "waterfront-grade.lmg         -0.3237     *   -0.3313 -0.3141\n",
       "view-condition.lmg            0.0506     *    0.0440  0.0568\n",
       "view-grade.lmg               -0.2769     *   -0.2892 -0.2650\n",
       "condition-grade.lmg          -0.3275     *   -0.3342 -0.3214\n",
       "                                                            \n",
       "bedrooms-bathrooms.last       0.0101     *    0.0049  0.0205\n",
       "bedrooms-sqft_living.last    -0.2556     *   -0.2794 -0.2415\n",
       "bedrooms-sqft_lot.last       -0.0060         -0.0128  0.0044\n",
       "bedrooms-floors.last          0.0096     *    0.0038  0.0196\n",
       "bedrooms-waterfront.last     -0.0287     *   -0.0402 -0.0157\n",
       "bedrooms-view.last           -0.0782     *   -0.0950 -0.0596\n",
       "bedrooms-condition.last      -0.0893     *   -0.1025 -0.0750\n",
       "bedrooms-grade.last          -0.4647     *   -0.4884 -0.4365\n",
       "bathrooms-sqft_living.last   -0.2658     *   -0.2882 -0.2509\n",
       "bathrooms-sqft_lot.last      -0.0161     *   -0.0225 -0.0113\n",
       "bathrooms-floors.last        -0.0006         -0.0027  0.0010\n",
       "bathrooms-waterfront.last    -0.0388     *   -0.0472 -0.0282\n",
       "bathrooms-view.last          -0.0883     *   -0.1064 -0.0715\n",
       "bathrooms-condition.last     -0.0994     *   -0.1111 -0.0854\n",
       "bathrooms-grade.last         -0.4749     *   -0.4970 -0.4516\n",
       "sqft_living-sqft_lot.last     0.2497     *    0.2348  0.2712\n",
       "sqft_living-floors.last       0.2652     *    0.2486  0.2881\n",
       "sqft_living-waterfront.last   0.2270     *    0.2099  0.2496\n",
       "sqft_living-view.last         0.1774     *    0.1514  0.2064\n",
       "sqft_living-condition.last    0.1663     *    0.1419  0.1998\n",
       "sqft_living-grade.last       -0.2091     *   -0.2420 -0.1655\n",
       "sqft_lot-floors.last          0.0155     *    0.0096  0.0215\n",
       "sqft_lot-waterfront.last     -0.0227     *   -0.0313 -0.0106\n",
       "sqft_lot-view.last           -0.0722     *   -0.0920 -0.0556\n",
       "sqft_lot-condition.last      -0.0833     *   -0.0960 -0.0672\n",
       "sqft_lot-grade.last          -0.4588     *   -0.4802 -0.4345\n",
       "floors-waterfront.last       -0.0383     *   -0.0474 -0.0267\n",
       "floors-view.last             -0.0878     *   -0.1056 -0.0710\n",
       "floors-condition.last        -0.0989     *   -0.1100 -0.0856\n",
       "floors-grade.last            -0.4743     *   -0.4969 -0.4503\n",
       "waterfront-view.last         -0.0495     *   -0.0727 -0.0292\n",
       "waterfront-condition.last    -0.0606     *   -0.0764 -0.0404\n",
       "waterfront-grade.last        -0.4360     *   -0.4658 -0.4090\n",
       "view-condition.last          -0.0111         -0.0328  0.0126\n",
       "view-grade.last              -0.3865     *   -0.4203 -0.3528\n",
       "condition-grade.last         -0.3754     *   -0.4077 -0.3519\n",
       "                                                            \n",
       "bedrooms-bathrooms.first     -0.1086     *   -0.1168 -0.1039\n",
       "bedrooms-sqft_living.first   -0.2155     *   -0.2230 -0.2082\n",
       "bedrooms-sqft_lot.first       0.0629     *    0.0559  0.0690\n",
       "bedrooms-floors.first         0.0161     *    0.0080  0.0217\n",
       "bedrooms-waterfront.first     0.0559     *    0.0466  0.0625\n",
       "bedrooms-view.first           0.0083         -0.0004  0.0163\n",
       "bedrooms-condition.first      0.0733     *    0.0667  0.0779\n",
       "bedrooms-grade.first         -0.2242     *   -0.2332 -0.2158\n",
       "bathrooms-sqft_living.first  -0.1069     *   -0.1119 -0.0999\n",
       "bathrooms-sqft_lot.first      0.1715     *    0.1663  0.1771\n",
       "bathrooms-floors.first        0.1247     *    0.1201  0.1308\n",
       "bathrooms-waterfront.first    0.1645     *    0.1594  0.1698\n",
       "bathrooms-view.first          0.1169     *    0.1101  0.1236\n",
       "bathrooms-condition.first     0.1819     *    0.1778  0.1866\n",
       "bathrooms-grade.first        -0.1156     *   -0.1238 -0.1076\n",
       "sqft_living-sqft_lot.first    0.2784     *    0.2743  0.2822\n",
       "sqft_living-floors.first      0.2316     *    0.2261  0.2365\n",
       "sqft_living-waterfront.first  0.2714     *    0.2648  0.2772\n",
       "sqft_living-view.first        0.2238     *    0.2181  0.2307\n",
       "sqft_living-condition.first   0.2888     *    0.2847  0.2918\n",
       "sqft_living-grade.first      -0.0087     *   -0.0136 -0.0039\n",
       "sqft_lot-floors.first        -0.0468     *   -0.0518 -0.0425\n",
       "sqft_lot-waterfront.first    -0.0070     *   -0.0116 -0.0036\n",
       "sqft_lot-view.first          -0.0546     *   -0.0594 -0.0499\n",
       "sqft_lot-condition.first      0.0104     *    0.0084  0.0126\n",
       "sqft_lot-grade.first         -0.2870     *   -0.2905 -0.2832\n",
       "floors-waterfront.first       0.0398     *    0.0344  0.0449\n",
       "floors-view.first            -0.0078     *   -0.0145 -0.0007\n",
       "floors-condition.first        0.0572     *    0.0534  0.0610\n",
       "floors-grade.first           -0.2403     *   -0.2448 -0.2344\n",
       "waterfront-view.first        -0.0476     *   -0.0535 -0.0414\n",
       "waterfront-condition.first    0.0174     *    0.0139  0.0224\n",
       "waterfront-grade.first       -0.2800     *   -0.2861 -0.2730\n",
       "view-condition.first          0.0650     *    0.0604  0.0691\n",
       "view-grade.first             -0.2325     *   -0.2390 -0.2251\n",
       "condition-grade.first        -0.2975     *   -0.3018 -0.2932\n",
       "\n",
       "* indicates that CI for difference does not include 0. \n",
       "CAUTION: Bootstrap confidence intervals can be somewhat liberal. "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Np9yByzl3nGK6czc6WskndePQW6LVW9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\nCRBAkAABBAkQQJAAAQQJEPAf+ojgjhz3mAAAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"with 95% bootstrap confidence intervals\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boot <- boot.relimp(mm1, b = 50, type = c(\"lmg\", \n",
    "                                               \"last\", \"first\"), rank = TRUE, \n",
    "                    diff = TRUE, rela = TRUE)\n",
    "booteval.relimp(boot) # print result\n",
    "plot(booteval.relimp(boot,sort=TRUE)) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "086333f7",
   "metadata": {},
   "source": [
    "Let's switch focus to p-values.\n",
    "\n",
    "So, when the sample size is large, p-values become essentially meaningless. We can either use the feature importance metrics from above or we can investigate how the p-values depend on the sample size. See the paper I posted on canvas. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "47777d70",
   "metadata": {},
   "outputs": [],
   "source": [
    "getpvalue <- function(x)  {\n",
    "  out <- t.test(x, alternative=\"greater\")$p.value\n",
    "}\n",
    "gettvalue <- function(x)  {\n",
    "  out <- t.test(x, alternative=\"greater\")$stat\n",
    "}\n",
    "# Testing if a mean of a vector is 0 and increasing the sample size (length) of the vector\n",
    "nuse <- c(100,300,500,1000,2500,5000,10000) # sample sizes\n",
    "muse <- c(0,0.01,0.05,0.1,0.25)             # mean values\n",
    "B    <- 500\n",
    "Pmat <- list()\n",
    "for (mn in (1:length(muse))) {\n",
    "  Pmat[[mn]] <- matrix(0,B,length(nuse))\n",
    "  for (nn in (1:length(nuse))) {\n",
    "     X <- matrix(rnorm(nuse[nn]*B,mean=muse[mn]),B,nuse[nn])\n",
    "     Pmat[[mn]][,nn] <- apply(X,1,getpvalue) \n",
    "            }\n",
    "          }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "1a3e391f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>mu</th><th scope=col>n</th><th scope=col>meanval</th><th scope=col>upper</th><th scope=col>lower</th><th scope=col>sd</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0</td><td> 100</td><td>0.5014948</td><td>0.9680348</td><td>0.03215405</td><td>0.2854941</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>0</td><td> 300</td><td>0.4948069</td><td>0.9718056</td><td>0.02086150</td><td>0.2872153</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>0</td><td> 500</td><td>0.4774176</td><td>0.9701798</td><td>0.02096263</td><td>0.2967088</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>0</td><td>1000</td><td>0.4729536</td><td>0.9774313</td><td>0.04561669</td><td>0.2886345</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>0</td><td>2500</td><td>0.4914866</td><td>0.9619954</td><td>0.02848797</td><td>0.2789043</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>0</td><td>5000</td><td>0.5154574</td><td>0.9748849</td><td>0.02461024</td><td>0.2930485</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 6\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & mu & n & meanval & upper & lower & sd\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 0 &  100 & 0.5014948 & 0.9680348 & 0.03215405 & 0.2854941\\\\\n",
       "\t2 & 0 &  300 & 0.4948069 & 0.9718056 & 0.02086150 & 0.2872153\\\\\n",
       "\t3 & 0 &  500 & 0.4774176 & 0.9701798 & 0.02096263 & 0.2967088\\\\\n",
       "\t4 & 0 & 1000 & 0.4729536 & 0.9774313 & 0.04561669 & 0.2886345\\\\\n",
       "\t5 & 0 & 2500 & 0.4914866 & 0.9619954 & 0.02848797 & 0.2789043\\\\\n",
       "\t6 & 0 & 5000 & 0.5154574 & 0.9748849 & 0.02461024 & 0.2930485\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 6\n",
       "\n",
       "| <!--/--> | mu &lt;dbl&gt; | n &lt;dbl&gt; | meanval &lt;dbl&gt; | upper &lt;dbl&gt; | lower &lt;dbl&gt; | sd &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 1 | 0 |  100 | 0.5014948 | 0.9680348 | 0.03215405 | 0.2854941 |\n",
       "| 2 | 0 |  300 | 0.4948069 | 0.9718056 | 0.02086150 | 0.2872153 |\n",
       "| 3 | 0 |  500 | 0.4774176 | 0.9701798 | 0.02096263 | 0.2967088 |\n",
       "| 4 | 0 | 1000 | 0.4729536 | 0.9774313 | 0.04561669 | 0.2886345 |\n",
       "| 5 | 0 | 2500 | 0.4914866 | 0.9619954 | 0.02848797 | 0.2789043 |\n",
       "| 6 | 0 | 5000 | 0.5154574 | 0.9748849 | 0.02461024 | 0.2930485 |\n",
       "\n"
      ],
      "text/plain": [
       "  mu n    meanval   upper     lower      sd       \n",
       "1 0   100 0.5014948 0.9680348 0.03215405 0.2854941\n",
       "2 0   300 0.4948069 0.9718056 0.02086150 0.2872153\n",
       "3 0   500 0.4774176 0.9701798 0.02096263 0.2967088\n",
       "4 0  1000 0.4729536 0.9774313 0.04561669 0.2886345\n",
       "5 0  2500 0.4914866 0.9619954 0.02848797 0.2789043\n",
       "6 0  5000 0.5154574 0.9748849 0.02461024 0.2930485"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### Summarizing the results from the B runs above\n",
    "Muse <- rep(muse,each=length(nuse))\n",
    "Nuse <- rep(nuse,length(muse))\n",
    "MM <- 0\n",
    "MU <- 0\n",
    "ML <- 0\n",
    "MS <- 0\n",
    "for (mn in (1:length(muse))) {\n",
    "    MM <- c(MM,apply(Pmat[[mn]],2,mean))\n",
    "    MS <- c(MS,apply(Pmat[[mn]],2,sd))\n",
    "    MU <- c(MU,apply(Pmat[[mn]],2,quantile, probs=.975)) # 95perc interval\n",
    "    ML <- c(ML,apply(Pmat[[mn]],2,quantile, probs=.025)) }\n",
    "MM <- MM[-1]\n",
    "MU <- MU[-1]\n",
    "ML <- ML[-1]\n",
    "MS <- MS[-1]\n",
    "df <- as.data.frame(cbind(Muse,Nuse,MM,MU,ML,MS))\n",
    "names(df) <- c(\"mu\",\"n\",\"meanval\",\"upper\",\"lower\",\"sd\")\n",
    "head(df)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ec42f96",
   "metadata": {},
   "source": [
    "Let's visualize how the p-values depend on the sample size and the effect size (true vector mean). \n",
    "Notice how rapidly the p-values approach 0 as the sample size grows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "0a57d874",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qRfGIsaAyFZDcuxBNtX2MUyIP2CWNQYykK6J4M0JumsaqHFBNtX2MUyIP38WNQY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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(data = df, aes(x = n, group = mu)) + \n",
    "  geom_line(aes(x = n, y = (meanval), color = mu), size = 1) +\n",
    "  geom_ribbon(aes(y = (meanval), ymin = meanval-sd, ymax = meanval+sd, fill = mu), alpha = .2) +\n",
    "  xlab(\"sample size\") +\n",
    "  ylab(\"p-value\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "238f5194",
   "metadata": {},
   "source": [
    "Let's investigate the pricing data using the same technique. We will chart both the p-value and coefficient value evolution as a function of sample size. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "201dbdaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "nuse <- c(150,300,500,1000,5000,10000,15000)\n",
    "B    <- 250\n",
    "mm0<-lm(price~sqft_living+bedrooms+condition+grade,data=kc5)\n",
    "Pmat <- list()\n",
    "Coefmat <- list()\n",
    "for (zz in (1:(dim(summary(mm0)$coef)[1]-1))) {\n",
    "    Pmat[[zz]] <- matrix(0,B,length(nuse))\n",
    "    Coefmat[[zz]] <- Pmat[[zz]] }\n",
    "#\n",
    "for (bb in (1:B)) {\n",
    "  for (nn in (1:length(nuse))) {\n",
    "     ii <- sample(seq(1,dim(kc5)[1]),nuse[nn])\n",
    "     mm<-lm(price~sqft_living+bedrooms+condition+grade,data=kc5,subset=ii)\n",
    "     ms <- summary(mm)$coef[-1,]\n",
    "     for (zz in (1:(dim(summary(mm)$coef)[1]-1))) {\n",
    "        pv <- log10(ms[zz,4])\n",
    "        if (pv==-Inf) { pv <- -325}\n",
    "        Pmat[[zz]][bb,nn] <- pv\n",
    "        Coefmat[[zz]][bb,nn] <- ms[zz,1] }\n",
    "      } }\n",
    "          \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "0f6095f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "np <- length(Pmat) # number of coefficients\n",
    "Nuse <- rep(nuse,np)\n",
    "feature <- rep(c(1,2,3,4),each=length(nuse))\n",
    "MM <- 0\n",
    "MU <- 0\n",
    "ML <- 0\n",
    "MS <- 0\n",
    "CM <- 0\n",
    "CU <- 0\n",
    "CL <- 0\n",
    "CS <- 0\n",
    "for (mn in (1:np)) {\n",
    "    MM <- c(MM,apply((Pmat[[mn]]),2,mean))\n",
    "    MS <- c(MS,apply((Pmat[[mn]]),2,sd))\n",
    "    MU <- c(MU,apply((Pmat[[mn]]),2,quantile, probs=.975))\n",
    "    ML <- c(ML,apply((Pmat[[mn]]),2,quantile, probs=.025)) \n",
    "    CM <- c(CM,apply((Coefmat[[mn]]),2,mean))\n",
    "    CS <- c(CS,apply((Coefmat[[mn]]),2,sd))\n",
    "    CU <- c(CU,apply((Coefmat[[mn]]),2,quantile, probs=.975))\n",
    "    CL <- c(CL,apply((Coefmat[[mn]]),2,quantile, probs=.025)) }\n",
    "MM <- MM[-1]\n",
    "MU <- MU[-1]\n",
    "ML <- ML[-1]\n",
    "MS <- MS[-1]\n",
    "CM <- CM[-1]\n",
    "CU <- CU[-1]\n",
    "CL <- CL[-1]\n",
    "CS <- CS[-1]\n",
    "#\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "11b665e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S9+UnPiIURCkRSpYnOXfpn0KJKpSd2KtFm6JLqKkFqlEAnFMQW3uUuaFCIxqBBJ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\nAgD/H/2cRw9pe9LoAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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CAsrM9TCkUCSTQCFqnukoGwsD5PKRQJ\nJBFYpPpLBsLC+jylUCSQRECR5l0yEBbW5ymFIoEkQok0+5KBsLA+TykUCSQRQiTIJQNhYX2e\nUigSSKK5IsEuGQgL6/OUQpFQFs0QCXrJQFhYn6cUigSSqFYk+CUDYWF9nlIoEkiiGpGaXDIQ\nFtbnKYUigSQqFanZJQNhYX2eUigSSKISkZpeMhAW1ucphSKBJJosUutLBsLC+jylUCSQRJNE\n6nHJQFhYn6cUigSSSBWp1yXzlJKnCmrfGmZEqpZIFKnnJfOUkqcKat8aVkSa5VGk1/cxsT5P\nKRQJ59GhSNBLtVulNRbW5ymFIuE82hUJepkOq7TGwvo8pVAknEdPIkEv0fEqrbGwPk8pFAnn\n0UYk6OU5XSVESp4qqH1rLC/SfI1GkaDXRqwSIiVPFdS+NRYXCaBRqF2YWJ+nFIoE8WjSYYII\nlJKnCmrfGguLBJBowmGCCJSSpwpq3xrLioSQaMJhggiUkqcKat8ai4oEkWjCYYIIlJKnCmrf\nGguKBJJowmGCCJSSpwpq3xrLiYSSaMJhggiUkqcKat8ai4mEs0g/TBCBUvJUQe1bYymRcBJN\nOEwQgVLyVEHtW2MhkYASTThMEIFS8lRB7VtjEZGgEk04TBCBUvJUQe1bw6xIyMMEESglTxXU\nvjVMioQ+TBCBUvJUQe1bw5xILQ4TRKCUPFVQ+9YwJVKrwwQRKCVPFdS+NZYQCSvRhMMEESgl\nTxXUvjWsiNT0MEEESslTBbVvDSMitT1MEIFS8lRB7VvDhkiNDxNEoJQ8VVD71lhAJLxHkXZh\nYn2eUigSzqNIuzCxPk8pFAnnUaRdmFifp5RoIsl8dItP7NLnf4CQpix+i9TjbyUQgVLyVEHt\nW6O/SA08irQLE+vzlEKRcB5F2oWJ9XlKoUg4jyLtwsT6PKVQJH5TyuVS8lRB7Vuju0gtPIq0\nCxPr85RCkfodJlMWCTFRBbVvjeVE6niYTFkkxEQV1L41FhOp52EyZZEQE1VQ+9boLVITjyLt\nwsT6PKXkFgl6lKF2YWJ9nlJSiwQ9yU+G2oWJ9XlKySwS9CCfQloTKCVPFdS+NShSypQ8VVD7\n1ugsUpt7dpF2YWJ9nlIoEpBAuzCxPk8pFAlIoF2YWJ+nFIoEJNAuTKzPU0pKkRp5FGkXJtbn\nKYUiAQm0CxPr85RCkYAE2oWJ9XlKoUhAAu3CxPo8pWQUqc0T7T4Zahcm1ucpJa9I0GPcDmlN\noJQ8VVD71qBIKVPyVEHtW4MipUzJUwW1bw2KlDIlTxXUvjUoUsqUPFVQ+9boLxL0FHdCWhMo\nJU8V1L41KFLKlDxVUPvW6ClSs3t2kXZhYn2eUmaIdH0+DGfH/sOLVfH+KVLKlDxVpM2uhluO\nWlGuBUVKmZKnijj+U+v3IBL0EHdDWhMoJU8VafubG6Sby2G4vBl/4c3FMKyuNv/hwabNW29X\n59vvSJGY0jHERBVdpLs7eOOHSq/vfmG4OiLS+XC59Y4UiSk9Q0xUkTZ7p8rzW3PWV8OL9fps\neLVev310aFukq513pEhM6Rlioooq0tnGl4vxx+vXz8+PinS9944UiSn9QkxUUUUa7rl98/zh\nrQOR1rvvuKxI7TyKtAsT6/OUghPpcjh78fqaIjUnUEqeKqpIZ8POT292RXryausdj/5Z8xXa\nIPekSLZS8lQRxz+u/2p8DOHVcD7+9M365uljpNXwavunW+9IkZjSM8REFVWkm7tHtYe3oylP\nHyOt7n/6/Emkp3ekSEzpGWKiiirS+vpyGM7fjG/dvTH+4otRpPXVani+9THS1jsuLxL0CPdD\nWhMoJU8V1L41KFLKlDxVUPvWoEgpU/JUQe1bo59IDT9EirQLE+vzlGJVpBcXtx9anZ94aEJA\n7kmRbKXkqQKxZAJ7It2c3T3+Nz6iXojcs+09u0i7MLE+Tyk2Rbq8exL56U87nUbuSZFspeSp\nghJFY0+kh0fNy79EUO5JkWyl5KnSRBP9PShSjpQ8VUp3fNySYpHu79pdjV8QWIbckyLZSslT\npXTHxyUpFun++UTD6ro0TO65EQl6gIchrQmUkqdK6Y6PO1Is0nr9/GwYzq5OvcTDaeSebW+Q\nIu3CxPo8pcwV6Rf3OeZIhUi1yD0pkq2UPFWEyf6CxK4iFIkpy4WYqCJM9ucldg2peNRO/oJa\nihQjJU8VYbI/J7GvBEViylIhJqoIk/3fEqImukgbrs+flzh0h9yTItlKyVNFmOz/kpigyYT3\nuBmKTZJ7UiRbKXmqCJP9WYkpmkx4jyZ37aDndySkNYFS8lQRJvs/JUr3f1yYV0PxN4iRe7a9\nQYq0CxPr85RSL9L/kCjd/6kHG65K/yC5J0WylZKnijDZn5Eo3f9xkVbFHlEkVyl5qgiT/e8S\npfvv9QlZimQqJU8VYbL/TaJ0/xQpZUqeKsJkf1qidP/bIg3bUKTIKXmqCJP9KQmKxBQrISaq\nCJP9rxJzRJqF3LOtR5F2YWJ9nlLqRfovEqX7p0gpU/JUESb7kxKl+98X6arNXTuKZCslTxVh\nsv9ZonT/e8JcNfoYiSLZSslTRZjsT0iU7n9PmNXw9ny4vjlHv0AkRbKVkqeKMNkflyjd/+HL\ncT0fXq9v0C8QSZFspeSpIkz2P0mU7v9QpNfDC/yzvymSrZQ8VYTJ/phE6f73hLkYXl0PZ+s3\nFCl2Sp4qwmT/o0Tp/veEGQ06Hx9rAL9AZFuPIu3CxPo8pdSL9B8kSve/f8vz+uzuW2min/1N\nkWyl5KkiTPbfS5Tuf0+k8u+L9IDckyLZSslTRZjsv5Mo3f/+gw1nr0v/hHvknhTJVkqeKsJk\n/61E6f73RDobhtXz8tcrXlMkXyl5qgiT/TcSpfvf/xjp+mo1DBfFn46lSL5S8lQRJvuvJUr3\nf+Rh7jdXw3D2qvQPkntSJFspeaoIk/1XEqX7P/4CkS2eawc9vaMhrQmUkqeKMNkfkSjd/7Fb\npMvbW6QXpX+Q3LOtR5F2YWJ9nlLqRfphidL9H/0Y6bLBx0jQwzse0ppAKXmqCJP9IYnS/R8+\nanf2osmjdtDDOx7SmkApeaoIk/1BidL9738e6aLV55Ggh3c8pDWBUvJUESb7LyVK97//PWRL\nf/8jck+KZCslTxVhsv9ConT/3V6zAXp4x0NaEyglTxVhsj8gUbp/ipQyJU8VYbLfL1G6/4ki\nrW7Zf3u1/YsUyVVKnirCqP+5RBuRVo8/bL29+51f5J5tPYq0CxPr85RSL9I/k6BITLESYqKK\nsOp/KjFTpIenBq12LTkm0t63IpN7UiRbKXmqCNv/JxJzRFqdfO3voyI9foj0kRE55v+W/n8R\n0pp/LFH6h20L82LLo93n2p28RZr6YMP/gf4ldCKkNYFS8lQRtv99EnNEWp98Ga6jHyNRJL8p\neaoI2/9eiR0pJnwxxIwHG4pEeh96eMdDWhMoJU8VYdXfI7GniOrJwYvoryZ/jESR/KbkqSJs\n/7slZop04kX0T4m09cid3PN9imQqJU8VYfvfJSF7ooq02nuU4fHXH57NsP329hMbKJKrlDxV\nNAHW37nPFE/Udyj/EvMH5J7vtzUp0C5MrM9TSr1I/0hi14riBxsuhtovpJB7UiRbKXmqCJP9\nDgnZk0P23uF6dX5dLtGI3JMi2UrJU0WY7LdLyJ4ccnDXrs137KNItlLyVBEm+w8l9hQxJFJL\nkwLtwsT6PKXUi/QPJGaKVI/ckyLZSslTRZjs35fYdgT3zIYJyD0pkq2UPFWEyf49idL9H4j0\n4mL8XmPl395F7kmRbKXkqSJM9u9KlO5//1WEzu5uxwb0dzV/v61JgXZhYn2eUupF+jsSpfvf\nE+lyuBo/KfsK/V3NKZKtlDxVhMn+bYnS/R95ZsPDP2XIPSmSrZQ8VYTJ/i2J0v1TpJQpeaoI\nk/02idL9H79rd4X+rubvtzUp0C5MrM9TSr1I3ypRuv/9BxvuvxxpVfxEIbknRbKVkqeKMNlv\nkSjd/8FduOfjN6S4Kn/qqtyTItlKyVNFmOw3S5Tuv+MnZCmSnZQ8VYTJfpNE6f67itRMpUC7\nMLE+Tyn1Iv1NidL9b4t095nYdk9abWhSoF2YWJ+nlHqRvlHCukhtTAq0CxPr85RSL9I3SMwR\naRZyz/ffb6pSoF2YWJ+nlHqR/oZE6f4XEKmBSYF2YWJ9nlLqRfrrEqX73xfpYvNlTGdNPo/U\nzKRAuzCxPk8p9SL9NYnS/R++rt3dr7Z5ZkMzlQLtwsT6PKXUi/RXJUr3f/C6dndfP/G23YMN\nTUwKtAsT6/OUUi/SX5Eo3f+J17VrLhLWpEC7MLE+Tyn1Iv1lidL9H7yu3eXNen1z1eTrkdqZ\nFGgXJtbnKaVepK+XKN3/weva3T9ptfhrzeWeR0RCmhRoFybW5ymlXqSvkyjd//5duJuruyet\nlr9KpNzzmEhAkwLtwsT6PKXUi/S1EqX7X+LzSHiTAu3CxPo8pdSL9JckSve/qEgwkwLtwsT6\nPKXUi/Q1EqX77/5cuyYmBdqFifV5SqkX6aslnIkEUinQLkysz1NKvUhfJTFHpLM59/PknqdF\ngpgUaBcm1ucppV6kr5Qo3f/BLVK5QhvknoJICJMC7cLE+jyl1Iv0FyVK929AJIBJgXZhYn2e\nUupF+gqJ0v1vi3M+DP0/RoKYFGgXJtbnKaVepL8gMUekh6c1dBdptkmBdmFifZ5S6kX68xJz\nRDpb6K7dfJMC7cLE+jyl1Iv05yRK92/hY6T5JgXahYn1eUqpF+nPSpTu34pI80wKtAsT6/OU\nUi/Sn5Eo3b+JBxtmCxVoFybW5ymlXqQ/LTFHpOUebJjrU6BdmFifp5R6kb5cYo5I65qvjH1A\n7lksUplQgXZhYn2eUupF+lMSO1LY+mbMc5h3mCACpeSpIkz2T0rsKaJ60vGbMSOoO0wQgVLy\nVBEm+2USM0Vq+s2YcRQeJohAKXmqCJP9ExKyJ6pITb8ZM5yphwkiUEqeKupw//g+UzxR36Hp\n95BtRqRdmFifp5R6kb5UotCjGCK9/0sbnxqTZ32eUupF+mMSM0Vq+82YG4v0APQ6HVRpjYX1\neUqpF+mPShR61PebMXcSqZVPedbnKaVepC+RKPSo7zdj7isS3Kc86/OUUi/SH5Eo9MjLJ2Rn\niIQTKs/6PKXUi/SHJbYUmfSUuTwi3dPukoGwsD5PKfUi/SGJ0v2feMniQHftToC/ZCAsrM9T\nSr1IXyxRuv9TL6If4MGGSQAvGQgL6/OUUi/SF0mU7v/g4e/zW4Wuz10//F0B4pKBsLA+Tyn1\nIn2hROn+F/tGY1Bmi/TAnEsGwsL6PKXUi/QHJUr3T5GOUXXJQFhYn6eUepH+gETp/nnXTqLo\nkoGwsD5PKfUi/X6J0v1nf7BhEtMuGQgL6/OUUi/S75Mo3X/ah78ryLM+Tyn1Iv1eidL9p/uE\nbI+UlsPAQJFu+QKJ0v1TpCVTKoaBgSLd8nskSve/K9KL1fjjm8vyl2ygSC1ToMt7uiqtMS7S\n50uU7n9HpPNhuFNoNVyV/jkUyUQKaH0gjIv0eRKl+98W6dWwen33xpvV8Kr0D5J7olZ2AgcT\nt5VCkW753RKl+999yeLX92+99vHiJ48EmniflEDP8q0X6XdJlO5/70X0j7w5Ebknfgo7BJq4\nWZEqMC7S75Qo3f8pkValf5Dcs/EVCzTxSCJ1ud2rF+lzJUr3v3vX7uH5DNd8ilDslEBV6kX6\nHInS/W+L9OJRn8vHj5YmQ5E8pQSqUi/S75Ao3f/Ox0Kr4WJ8qeI3F8NZ6Z9DkVylBKpSL9Jn\nS5Tuf0ekx2+QVP6c1SkifechoMMMtAuKVEi9SL9dYpZI6/Wri1uNLoo/ibSeItIRjwiZS71I\nv02idP/dnmu39HmToNSL9FslSvffS6S7zoe3ywtfBOKfepE+S6J0/51Euqvc7n5yoLv8/Bip\nkHqRfotE6f77idTyMAPtgiIVUi/Sb5Yo3X+3u3ZNDzPQLihSIfUi/SaJ0v3zC/tSpgSqUi/S\nb5Qo3T9FSpkSqEq9SJ8pUbp/ipQyhc/+vuU3SJTunyKlTOEX9t3y6yVK90+RIqbMXR8I4yJ9\nhkTp/imSv5T26wNhXKRPlyjdP0WylmJhfZ5S6kX6dRKl+6dIfVNmDwMDRbrl0yRK90+RkCkd\nhoGBIt3yayVK90+RppNnfZ5S6kX6NRKl+4eJJPNLnulzRKQ3v1pi5z0nWMJbpJOU/t0HwsJf\n455S6m+RPlViRxKKVEPtJQNhYX2eUupF+lUSO45QpAJmXzIQFtbnKaVepF8pUWoJRYJdMhAW\n1ucppV6kDb9inzpL0oqEv2QgLKzPU8pckaZAkQ5oeMlAWFifpxSKBCTQp0pNrM9TCkXqIVLP\nS+YpJU8VyLjzigS9VLtVWmNhfZ5SKFIDkaBX6ESV1lhYn6cUigQk0C5MrM9TSg+RJuBapKmH\nCSJQSp4qqH1reBSp+DBBBErJUwW1bw1PIlUfJohAKXmqoPat0Umk95r4M/UwQQRKyVMFtW8N\nwyLhDhNEoJQ8VVD71rAnUoPDBBEoJU8V1L41zIjU8jBBBErJUwW1bw0rIjU9TBCBUvJUQe1b\nw4ZIjQ8TRKCUPFVQ+9awIFLzwwQRKCVPFdS+NZYXqcNhggiUkqcKat8avUQ6ZVKXwwQRKCVP\nFdS+NRYWqc9hMmWREBNVUPvWWFSkXofJlEVCTFRB7VtjQZH6HSZTFgkxUQW1b43FROp5mExZ\nJMREFdS+NRYSCXqUoXZhYn2eUjKLBD3Ip5DWBErJUwW1bw2KlDIlTxXUvjW6ifQeRTKUkqcK\nat8aS4gEPcetkNYESslTBbVvDYqUMiVPFdS+NShSypQ8VVD71lhAJOgxboe0JlBKniqofWtQ\npJQpeaqg9iREHogAAA/2SURBVK3RXyToKe6EtCZQSp4qqH1rUKSUKXmqoPat0U+k9yiSnZQ8\nVVD71uguEvQQd0NaEyglTxXUvjUoUsqUPFVQ+9agSClT8lRB7Vujt0jQM9wLaU2glDxVUPvW\noEgpU/JUQe1bo7NI0CPcD2lNoJQ8VVD71qBIKVPyVEHtW6OjSO9RJDMpeaqg9q3RVyToCR6E\ntCZQSp4qqH1rUKSUKXmqoPat0VUk6AEehrQmUEqeKqh9a1CklCl5qqD2rUGRUqbkqYLatwZF\nSpmSpwpq3xoUKWVKniqofWv0FOk96AEehrQmUEqeKqh9a/QU6SX0AA9DWhMoJU8V1L41KFLK\nlDxVUPvWoEgpU/JUQe1bgyKlTMlTBbVvDYqUMiVPFdS+NShSypQ8VVD71ugo0kuKZCYlTxXU\nvjW6itTMpEC7MLE+TykUCUigXZhYn6eUlCK1MinQLkysz1MKRQISaBcm1ucpJZ1ILymSnZQ8\nVVD71ugsUiOTAu3CxPo8pVAkIIF2YWJ9nlIoEpBAuzCxPk8pSUVqY1KgXZhYn6cUigQk0C5M\nrM9TSjaRXlIkQyl5qqD2rdFdpCYmBdqFifV5SqFIQALtwsT6PKWkFamFSYF2YWJ9nlIoEpBA\nuzCxPk8pFAlIoF2YWJ+nlGQivXzZ0qRAuzCxPk8pFAlIoF2YWJ+nFIoEJNAuTKzPU0pikfAm\nBdqFifV5SqFIQALtwsT6PKXkEuklRTKVkqcKat8ai4gENynQLkysz1NKapHQJgXahYn1eUrJ\nLRLYpEC7MLE+TykUCUigXZhYn6eU5CJhTQq0CxPr85SSXSSoSYF2YWJ9nlLSi4Q0KdAuTKzP\nUwpF6neYTFkkxEQV1L41Joq0umX/7e1fqxEJaFKgXZhYn6cUVyKtHn94env719ZVIuFMCrQL\nE+vzlEKRgCYF2oWJ9XlKoUgUabmUPFWwupwGIdJHRv7/LeNPjv/7gw/+3y0ffLD/71Pvz3/z\n35h/92LZWyTUbVKgv2BN/DXuKSXQLdIdcs+TImFMCrQLE+vzlEKRKNJyKXmqYHU5zeIiQUwK\ntAsT6/OUQpGAJgXahYn1eUpxJdLTsxm23577zAacSYF2YWJ9nlJ8iaQj96RItlLyVEHtW8OC\nSPNNCrQLE+vzlEKRgCYF2oWJ9XlKoUhAkwLtwsT6PKVQJIq0XEqeKqh9axgRaaZJgXZhYn2e\nUigS0KRAuzCxPk8pFIkiLZeSpwpq3xpmRJrlU6BdmFifpxSKBNQp0C5MrM9TCkUC6hRoFybW\n5ymFIgF9CrQLE+vzlEKRgDoF2oWJ9XlKoUhAnQLtwsT6PKVQJKBOgXZhYn2eUigS0KdAuzCx\nPk8pFAmoU6BdmFifpxSKBOQD/Pd3PlklREqeKqh9a0QRaQP0Cp2o0hoL6/OUQpEaiNTWpzzr\n85RCkdqJ1EinPOvzlEKRWosE1ynP+jylUKQ+IgF9yrM+TykUqatIG5peMhAW1ucphSIBmSrS\nhkaXDISF9XlKoUhAykTaAL9kICysz1MKRQJSI9I9uEsGwsL6PKVQJCAzRNqAuGQgLKzPUwpF\nAjJbpA3zLhkIC+vzlEKRgIBE2lB7yUBYWJ+nFIoEBCrSPcWXDISF9XlKoUhAWoi0oeCSgbCw\nPk8pFAlIO5E2TLpkICysz1MKRQLSWqQNedbnKYUiAekj0okU6CxsrM9TCkVqP/FFUxoNAwNF\nQkOR+qbMHgYGioSGIplImT4MDBQJDUUynAId3JGr0hqKVIHcs9/4EqS0Xx8IilSB3HPx8cVP\nQa4PBEWqQO4Jndohtie+aErV+kBQpArknthxHOBy4kumUCQ0FCllSkUIfuMYKBKQQBM3K1IF\nFKkCuWfjKxZo4pFE6nK7R5GAmN2F1ZRAVSgSkEC7oEiF5BLp3XebHmagXVCkQlKJ9O67bU0K\ntAuKVEgqkVqbFGgXFKmQXCK93Bbp3SdAhxloF9unQyaQTKQnk5Y+eBKLhCK9S40InGwiHb9D\nt9jx24UfI5WRTqRHaRocZqBd8MGGQvKJ9LKVRqF2QZEKySlSo8MMtAuKVEhCkdoRaBcUqRCK\nBCTQLijSIbIpFAmHr10YSDFXRbaBIlEkmylLVKl3RTZF+c+doEgpUxqFlG0cA0UCEmji1kUC\nbhwDRQISaOIGROq18S4hqH1rUKSUKXw5LjQUKXxKxfpAUKQK5J7ocezhdOL4FND6QFCkCuSe\nqJWdwMHE8SkN1weCIlUg92y5vJfmJg5PgS7v6aq0hiJVIPdcYHxeUyysz1MKRQLiVaSKYWCg\nSGgoUqcU1DAwUCQ0FKlBSsthYKBIaCjSzBToKJ4OrDEUCQ1Fmk6e9XlKoUhAmos05ZKBsLA+\nTykUCUhLkSZfMhAW1ucphSIBCfTlNSbW5ymFIgHp8kTPROvzlEKRgCBFqr5kICysz1MKRQIC\nEmneJQNhYX2eUigSkPkiAS4ZCAvr85RCkYDMEQl2yUBYWJ+nFIoEpFIk7CUDYWF9nlIoEpBy\nkRpcMhAW1ucphSIBKRKp1SUDYWF9nlIoEpCJIrW9ZCAsrM9TCkUCoovU4ZKBsLA+TynRRJL5\nYEH6NCS5iX2LBP2rL9Ff455Sot0iyT27iwS9VjtVWmNhfZ5SKFIrkaCX6bBKayysz1MKRWog\nEvQKnajSGgvr85RCkbAiQS+OVCVESp4qqH1rBBBJP0wQgVLyVEHtW8O3SBMPE0SglDxVUPvW\ncCtSyWGCCJSSpwpq3xoeRSo+TBCBUvJUQe1bw5dIlYcJIlBKniqofWu4EWnOYYIIlJKnCmrf\nGh5Emn2YIAKl5KmC2reGcZEwhwkiUEqeKqh9a5gVCXmYIAKl5KmC2reGRZHghwkiUEqeKqh9\naxgTqc1hggiUkqcKat8aZkRqeZggAqXkqYLat4YVkZoeJohAKXmqoPatYUSktocJIlBKniqo\nfWvYEKnxYYIIlJKnCmrfGiZEan2YIAKl5KmC2reGBZGaHyaIQCl5qqD2rWFApPaHCSJQSp4q\nqH1rLC9Sh8MEESglTxXUvjUWF6nHYYIIlJKnCmrfGkuL1OUwQQRKyVMFtW+NhUXqc5hMWSTE\nRBXUvjWWFanTYTJlkRATVVD71lhUpF6HyZRFQkxUQe1bY0mRuh0mUxYJMVEFtW+NBUXqd5hM\nWSTERBXUvjWWE6njYTJlkRATVVD71lhMpJ6HyZRFQkxUQe1bYymRoGcZaRcm1ucpJbdI0KMM\ntQsT6/OUklkk6EE+hbQmUEqeKqh9a1CklCl5qqD2rUGRUqbkqYLatwZFSpmSpwpq3xoUKWVK\nniqofWssIRL0HLdCWhMoJU8V1L41KFLKlDxVUPvWoEgpU/JUQe1bgyKlTMlTBbVvDYqUMiVP\nFdS+NRYQCXqM2yGtCZSSpwpq3xoUKWVKniqofWtQpJQpeaqg9q1BkVKm5KmC2rcGRUqZkqcK\nat8a/UWCnuJOSGsCpeSpgtq3BkVKmZKnCmrfGhQpZUqeKqh9a1CklCl5qqD2rUGRUqbkqYLa\nt0Z3kaCHuBvSmkApeaqg9q1BkVKm5KmC2rcGRUqZkqcKat8aFCllSp4qqH1rUKSUKXmqoPat\n0Vsk6BnuhbQmUEqeKqh9a1CklCl5qqD2rUGRUqbkqYLatwZFSpmSpwpq3xoUKWVKniqofWt0\nFgl6hPshrQmUkqcKat8aFCllSp4qqH1rUKSUKXmqoPatQZFSpuSpgtq3BkVKmZKnCmrfGn1F\ngp7gQUhrAqXkqYLatwZFSpmSpwpq3xoUKWVKniqofWtQpJQpeaqg9q3RVSToAR6GtCZQSp4q\nqH1r9BQJen5HQloTKCVPFdS+NfqJBD29oyGtCZSSpwpq3xrdRIIe3vGQ1gRKyVMFtW+NTiI1\nJtAueGDYENS+NShSypQ8VVD71qBIKVPyVEHtW4MipUzJUwW1bw2KlDIlTxXUvjUoUsqUPFVQ\n+9agSClT8lRB7VuDIqVMyVMFtW8NipQyJU8V1L41KFLKlDxVUPvWoEgpU/JUQe1bgyKlTMlT\nBbVvDYqUMiVPFdS+NShSypQ8VVD71pgo0uqW/bdX279IkVyl5KkC9uUk00RaPf6w9fZq510q\ne2IItAseGDYE6IoIRUqZkqcK0BWRepF2PaJIrlLyVAG6IjJDpMcPkT4y0uJ/jhAvzLxF4oMN\nPlPyVMHqcpoZHyNt/5si+UrJUwXoiogm0ub+G0UKlpKnCtyYE/CuXcqUPFWwupxmnkhbj9xV\n9sQQaBc8MGwIVpfTFD6zYbX99vYTGyiSq5Q8VeDGnIDPtUuZkqcKat8aFCllSp4qqH1rUKSU\nKXmqoPatQZFSpuSpgtq3BkVKmZKnCmrfGhQpZUqeKqh9a1CklCl5qqD2rUGRUqbkqYLatwZF\nSpmSpwpq3xoUKWVKniqofWvARDpFoK/4YxWLGKlCkabDKhYxUoUiTYdVLGKkCkWaDqtYxEiV\n5iIRkgGKRAgAikQIAIpECACKRAgAikQIgMYi7b5AijseXpZ5//Ve3NXa/N+equGqzlMVU1em\nrUh7r33njhMv5eeu1tNLQB2r4arOvSfmrgxFkjB3uepYrcOItFpTJH/svDCzictVSxiRjr1k\ntokqFEng8Y74em3kctUSTiRzV4YiCcRY3kg4ke5/sFOFImmYuly1GF1fDavtt+xUoUgapi5X\nLRSpNRRJIMbyRqKJZK8KRRJYbf1j43LVYnR9NTz+39q6Mnxmg0SIpwKMbP5vQ9QxWoXPtSME\nAEUiBABFIgQARSIEAEUiBABFIgQARSIEAEUiBABFIgQARbLGIFwS6b+RReGVsQZFcgmvjDUo\ni0t41frwfDWcvRjfeHMxDKur9Z0wF8PF+vpsuLi5/9n59fpepJvLYbi8Ofjdt/9tuOfgfcii\nUKQuXN2N/9aF1xsNrkYpbpUaXp3d/nA5/uxWi2F1cy/Sanyns4PfvSPS7vuQZaFIXRiG6/Wb\nYbVenw2v1uu3owejP69GpV5tfnZ+sz7fCHZ7CzS+cTW82P/dD3f7zofz/fchy0KRurAaLl/f\nv3n9+vn5Rp3r8Yf726BheHv7n8YbmPFnZ3eX5faO397vvhdp9Gj/fciyUKQuvL69H3Y2fgR0\nK8H9PbM7KR5/2Cjy8NbT/bfd3735+OnOo/33IcvC69CJt2fD6s16fTmcvXh9XSjS4+8ef+V6\nNX5MRZGMwevQjRePwtwcE+l6vGt3vn3X7ujvvvXo6u4XjrwPWQ5ejS6shjfrt5uHC96M982O\niHQ+/vrzzc+uRlle3d2D2/vd6weP9t+HLAtF6sLmAeznD28cFWl8+Pv+Zzd3D22Pjz/s/u7t\nh7/33ocsC0Xqw9VqWD0f37i8VebN0bt258Pl4wMK13fvdvC7dz6PtPc+ZFEokg34oIFzeP1s\nQJGcw+tnA4rkHF4/G1Ak5/D6EQKAIhECgCIRAoAiEQKAIhECgCIRAoAiEQKAIhEC4JcBvGfd\nhqlhuQoAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df <- as.data.frame(cbind(feature,Nuse,MM,MU,ML,MS,CM,CU,CL,CS))\n",
    "names(df) <- c(\"feature\",\"n\",\"pmean\",\"pupper\",\"plower\",\"psd\",\"cmean\",\"cupper\",\"clower\",\"csd\")\n",
    "#\n",
    "ggplot(data = df, aes(x = n, y=pmean, group = feature)) + \n",
    "  geom_line(aes(x = n, y = pmean, color = feature), size = 1) +\n",
    "  geom_ribbon(aes(y = (pmean), ymin = plower, ymax = pupper, fill = feature), alpha = .2) +\n",
    "  xlab(\"sample size\") +\n",
    "  ylab(\"log10(p-value)\")\n",
    "\n",
    "ggplot(data = df, aes(x = n, y=cmean, group = feature)) + \n",
    "  geom_line(aes(x = n, y = cmean, color = feature), size = 1) +\n",
    "  geom_hline(yintercept=0, color=\"darkorange\",linetype=\"dashed\") +\n",
    "  geom_ribbon(aes(y = (cmean), ymin = clower, ymax = cupper, fill = feature), alpha = .2) +\n",
    "  xlab(\"sample size\") +\n",
    "  ylab(\"Coefficient value\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "69046073",
   "metadata": {},
   "outputs": [],
   "source": [
    "# with extra noise\n",
    "kcn<-kc5\n",
    "kcn$noise1 <- rnorm(dim(kcn)[1])\n",
    "kcn$price <- kcn$price + rnorm(dim(kcn)[1],sd=.25) # add some noise to the problem, play with this to see what happens\n",
    "#\n",
    "nuse <- c(150,300,500,1000,5000,10000,15000)\n",
    "B    <- 250\n",
    "mm0<-lm(price~sqft_living+bedrooms+condition+grade+noise1,data=kcn)\n",
    "Pmat <- list()\n",
    "Coefmat <- list()\n",
    "for (zz in (1:(dim(summary(mm0)$coef)[1]-1))) {\n",
    "    Pmat[[zz]] <- matrix(0,B,length(nuse))\n",
    "    Coefmat[[zz]] <- Pmat[[zz]] }\n",
    "#\n",
    "np <- length(Pmat) # number of coefficients\n",
    "for (bb in (1:B)) {\n",
    "  for (nn in (1:length(nuse))) {\n",
    "     ii <- sample(seq(1,dim(kcn)[1]),nuse[nn])\n",
    "     mm<-lm(price~sqft_living+bedrooms+condition+grade+noise1,data=kcn,subset=ii)\n",
    "     ms <- summary(mm)$coef[-1,]\n",
    "     for (zz in (1:(dim(summary(mm)$coef)[1]-1))) {\n",
    "        pv <- log10(ms[zz,4])\n",
    "        if (pv==-Inf) { pv <- -325}\n",
    "        Pmat[[zz]][bb,nn] <- pv\n",
    "        Coefmat[[zz]][bb,nn] <- ms[zz,1] }\n",
    "      } }\n",
    "Nuse <- rep(nuse,np)\n",
    "feature <- rep(seq(1,np),each=length(nuse))\n",
    "MM <- 0\n",
    "MU <- 0\n",
    "ML <- 0\n",
    "MS <- 0\n",
    "CM <- 0\n",
    "CU <- 0\n",
    "CL <- 0\n",
    "CS <- 0\n",
    "for (mn in (1:np)) {\n",
    "    MM <- c(MM,apply((Pmat[[mn]]),2,mean))\n",
    "    MS <- c(MS,apply((Pmat[[mn]]),2,sd))\n",
    "    MU <- c(MU,apply((Pmat[[mn]]),2,quantile, probs=.975))\n",
    "    ML <- c(ML,apply((Pmat[[mn]]),2,quantile, probs=.025)) \n",
    "    CM <- c(CM,apply((Coefmat[[mn]]),2,mean))\n",
    "    CS <- c(CS,apply((Coefmat[[mn]]),2,sd))\n",
    "    CU <- c(CU,apply((Coefmat[[mn]]),2,quantile, probs=.975))\n",
    "    CL <- c(CL,apply((Coefmat[[mn]]),2,quantile, probs=.025)) }\n",
    "MM <- MM[-1]\n",
    "MU <- MU[-1]\n",
    "ML <- ML[-1]\n",
    "MS <- MS[-1]\n",
    "CM <- CM[-1]\n",
    "CU <- CU[-1]\n",
    "CL <- CL[-1]\n",
    "CS <- CS[-1]\n",
    "#          "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "4c4bab88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZPukLGTkPrpQzKQpKAk3wrWFkJWfPJJ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\nhLSYFjYknKT9MChJg5Tozw1qDqMc0m8vRQlJFuGMoCy2hQ0JJuk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7zwvTWRISI5FaXAyDkkR88xjTWRISPZFafAwDkkR9FybTWRD7TUlC\nctXiZBiMJPLbmVnOgthvShKSqxYvw0Ak0d8X0HAWxH5TkpBctbgZRi5JAkkjKSGhEqnFzzAA\nSZx3qjWbBbHflCQkVy2OhhFD2ktKSNwIZwQlUounYdSSWO+dbjULYr8pSUiuWlwNo5XEgiSW\nlJBQidTiaxilJB4kqaSEhEqkFmfD6CQxIQklJSRUIrV4G0YliQtJJikhoRKpxd0wGklsSCJJ\nCQmVSC3+hlFI4kOSSEpIqERqcTiMXJIAkkBSQkIlUovHYeSSJH8PPQtivylJSK5aXA7jW1JC\nQiVSi8thZJBqSUpIqERq8TmMa0kJCZVILU6HkUG6rSIpIaESqcXrMDJIVa5JCQmVSC1uh5FB\nqiEpIaESqcXvMDJIFSQlJFQitTgeRgbJXlJCQiVSi+dhZJDMJSUkVCK1uB5GBslaUkJCJVKL\n72FkkIwlJSRUIrU4H0YGyVZSQkIlUov3YWSQroWQSJISEiqRWtwPI4NkKSkhoRKpxf8wYkhW\nkhISKpFaFjCMCJKhpISESqSWJQwjgmQnKSGhEqllEcOIIJlJSkioRGpZxjAiSFaSEhIqkVoW\nMowIkpGkhIRKpJalDCOCZPOF2YSESqSWxQwjgmQiKSGhEqllOcOIIFlISkioRGpZ0DAiSAaS\nEhIqkVoWNIwMEl5SJEiZc8ytLO3NjAWZe9yJ5BXJVcuihhFdkeDXpEhXpNEhFGeJnkgtyxpG\nBgksKSGhEqllYcPIIGElJSRUIrUsbRgZJKikhIRKpJbFDSODhJSUkFCJ1LK8YWSQgJISEiqR\nWhY4jAwSTlJCQiVSyxKHkUGCSUpIqERqWeQwMkgoSQkJlUgtyxxGBgl0a6GEhEqkloUOI4OE\nkZSQUInUstRhxJD0khISKpFaFjuMCBJEUkJCJVLLcocRQUJISkioRGpZ8DAiSABJCQmVSC1L\nHkYESS8pIaESqWXRw4ggqSUlJFQitSx7GBEkraSEhEqkloUPI4KklJSQUInUsvRhRJB0khIS\nKpFaFj+MCJJKUkJCJVLL8ocRQdJISkioRGpZ/jAySApJCQmVSC0BhpFBkktKSKhEaokwjAyS\nWFJCQiVSS4hhZJCkkhISKpFaYgwjgySUlJBQidQSZBgZJJmkhIRKpJYow8ggiSQlJFQitYQZ\nRgZJIikhoRKpJc4wMkgCSQkJlUgtgYaRQeJLSkioRGqJNIwMEltSQkIlUkuoYWSQuDfpSkio\nRGoJNcxGBokpKSGhEqkl1DAbwhs2j0BiSEpIqERqCTXMhvLW52pJCQmVSC2hhmla7CUlJFQi\ntYQapm0xl5SQUInUEmqYbYu1pISESqSWUMPsWowlJSRUIrWEGuaxxVZSQkIlUkuoYfYtppIS\nEiqRWkINc2ixlJSQUInUEmqYTouhpISESqSWUMN0W+wkJSRUIrWEGkYPiSIpIaESqSXUMEct\nZpISEiqRWkINc9xiJSkhoRKpJdQwvRYjSQkJlUgtoYbpt9hISkioRGoJNcxJi4mkhIRKpJZQ\nw5y2WEhKSKhEagk1zECLgaSEhEqkllDDDLXgJSUkVCK1hBpmsAUuKSGhEqkl1DDDLWhJCQmV\nSC2hhhlpkUtKSKaJ1BJqmLEWrKSEhEqkllDDjLaIIQ1JSkioRGoJNcx4C1JSQkIlUkuoYQot\nQEkJCZVILaGGKbXgJCUkVCK1hBqm2AKTlJBQidQSaphyC0pSQkIlUkuoYSZaQJISEiqRWkIN\nM9WCkZSQUInUEmqYyRaIpISESqSWUMNMtyAkJSRUIrWEGsYK0rGkhIRKpJZQwxBaAJISEiqR\nWkINQ2nRS0pIqERqCTUMqUUtKSGhEqkl1DC0Fq2khIRKpJZQwxBblJISEiqRWkINQ23RSUpI\nqERqCTUMuUUlKSGhEqkl1DD0Fo2khIRKpJZQwzBaFJISEiqRWkINw2lRSJr4IColIblqCTUM\nq0UuaeKDqJSE5Kol1DC8FqmkfGiHSqSWUMMwW4SSEhIqkVpCDcNtSUioIylLpJZQw7BbEhLq\nSIoSqSXUMPyWhIQ6kpJEagk1jKAlIaGOpCCRWkINI2lJSKgjyU+kllDDiFoSEupIshOpJdQw\nspaEhDqS3ERqCTWMsCUhoY4kM5FaQg0jbUlIqCPJS6SWUMOIWxIS6kiyEqkl1DAJiRv4kWQl\nUkuoYeQtCQl1JDmJ1BJqGEVLQkIdSUYitYQaRtOSkFBHkp5ILaGGUbUkJNSRJCdSS6hhdC0J\nCXUkqYnUEmoYZUtCQh1JYiK1hBpG25KQUEeSlkgtoYZRtyQk1JEkJVJLqGH0LQkJdSQpidQS\nahhAS0JCHUlCIrWEGgbRkpBQR3I6kVpCDQNpSUioIzmZSC2hhsG0JKRlnS8fLaGGAbUEg7Te\n/rPJ7sfD7xkfyYlEagk1DKolFKSdm52edefnm4S0uJqFtQSCtN4kpEA1S2uJA6lnJyEtu2Zx\nLeEgPX6KtP83H2li8pFlMofcjmbuj2wXwRVpnVekpdcssCXWFenxZwlp2TVLbFk4pP3z3Akp\nUM0iW5YNaZ98aBeoZpktwSAdP9nQptaRjN8SapiENJTDKxu6P25T60jGbwk1DLwlBKRSqh3J\n8C2hhsG3JCTLRGoJNYxBS0IyTKSWUMNYtCQku0RqCTWMSUtCMkukllDD2LQkJKtEagk1jFFL\nQjJKpJZQw1i1JCSbRGoJNYxZS0IySaSWUMPYtSQki0RqCTWMYUtCMkikllDDWLYkJHwitYQa\nxrQlIcETqSXUMLYtCQmdSC2hhjFuSUjgRGoJNYx1S0LCJlJLqGHMWxISNJFaQg1j35KQkInU\nEmqYCi0JCZhILaGGqdGSkHCJ1BJqmCotCQmWSC2hhnHRgthvShKSq5ZQw7hoQew3JQnJVUuo\nYVy0IPabkoTkqiXUMC5aEPtNSUJy1RJqGBctiP2mJCG5agk1jIsWxH5TkpBctYQaxkULYr8p\nSUiuWkIN46IFsd+UJCRXLaGGcdGC2G9KEpKrllDDuGhB7DclCclVS6hhXLQg9puShOSqJdQw\nLloQ+01JQnLVEmoYFy2I/aYkIblqCTWMixbEflOSkFy1hBrGRQtivylJSK5aQg3jogWx35Qk\nJFctoYZx0YLYb0oSkquWUMO4aEHsNyUJyVVLqGFctCD2m5KE5Kol1DAuWhD7TUlCctUSahgX\nLYj9piQhuWoJNYyLFsR+U5KQXLWEGsZFC2K/KUlIrlpCDeOiBbHflCQkVy2hhnHRgthvShKS\nq5ZQw7hoQew3JQnJVUuoYVy0IPabkoTkqiXUMC5aEPtNSUJy1RJqGBctiP2m5MhWUAAAA5RJ\nREFUJCG5agk1jIsWxH5TkpBctYQaxkULYr8pSUiuWkIN46IFsd+UJCRXLaGGcdGC2G9KEpKr\nllDDuGhB7DclCclVS6hhXLQg9puShOSqJdQwLloQ+00JBNJYPmL5H6+cSLOEGsbJLAmJmEiz\nhBrGySwJiZhIs4QaxsksCYmYSLOEGsbJLKaQMplzSULKZABJSJkMIAkpkwEkIWUygCSkTAYQ\nQ0jrh9j91+2z3g3wOEf/xwVl+/GODbKsgQ6zuDo5dpDW+38sNOvOD+vTHxeU9eFjHhhkWQPt\nnLg7OQlpNO7OlTTrTRxI601CWljW3R9dnCt54kDqfbh+ZklIY9k/Ct9snJwreeJBcndyEtJY\nguxdm3iQdv/wM0tCKsbVuZLH6fKJsu7+zM8sCakYV+dKnoRknoQ0liB71yYcJH+zJKSxrDv/\n83Gu5HG6fKLsP1xfJydf2TCaGC8EaLP9eGMM5HSWfK1dJgNIQspkAElImQwgCSmTASQhZTKA\nJKRMBpCElMkAkpAyGUASUiYDSELylVXhhJR+LzNz8tz4SkJaaPLc+EpiWWjyvNXI8/Xq4kXz\nk9dPVqv11aYF82T1ZHN3sXryZvery7vNDtKbp6vV0zcnf/vh91a7nPyZzMxJSBVy1S7/g4VX\nWwZXDYoHUqv3Lh7+8bT51QOL1frNDtK6+UMXJ3/7CNLxn8nMnYRUIavV3eb1ar3ZXKze22ze\nbxw0ft5rSL23/dXlm83lFtjDFaj5ydXqRf9vPz7su1xd9v9MZu4kpApZr56+2v307tXzyy2d\nu+Yfu2vQavX+w281F5jmVxftSXl44Nf72ztIjaP+n8nMnYRUIa8eHoddNJ8BPSDYPTJrUez/\nsSXy+LPD47fjv739/Kl11P8zmbmTZ6JK3r9YrV9vNk9XFy9e3TEh7f9282/u1s3nVAnJXfJM\nVMqLPZg3Q5Dumod2l92HdoN/+8HRVfsvBv5MZs7k+aiQ9er15v3t0wWvm8dmA5Aum3//fPur\nqwbLe+0juN7f3jw66v+ZzNxJSBWyfQL7+eNPBiE1T3/vfvWmfWq7ef7h+G93n/7u/ZnM3ElI\nNXK1Xq2fNz95+kDm9eBDu8vV0/0TCnftHzv520dfR+r9mczMSUgekk8aLD55Bj0kIS0+eQY9\nJCEtPnkGPSQhLT55BjMZQBJSJgNIQspkAElImQwgCSmTASQhZTKAJKRMBpCElMkA8v8BF7Tv\nKoT+m+8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XNo0OB4kP6mJBGTGU2fbHg0vXHsQJ4rJYNkIgl0e2WSQIfGDI4H6W9IEjGZ0eQr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\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lKXSBbhLYekDswUhYZFWlPiEskivOWQ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\nlCQAUqQkAZAiJQmAFClJAKRISQLg/wMqPyJ+sCJFFQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "         \n",
    "df <- as.data.frame(cbind(feature,Nuse,MM,MU,ML,MS,CM,CU,CL,CS))\n",
    "names(df) <- c(\"feature\",\"n\",\"pmean\",\"pupper\",\"plower\",\"psd\",\"cmean\",\"cupper\",\"clower\",\"csd\")\n",
    "#\n",
    "ggplot(data = df, aes(x = n, y=pmean, group = feature)) + \n",
    "  geom_line(aes(x = n, y = pmean, color = feature), size = 1) +\n",
    "  geom_hline(yintercept=c(-2,-3), color=\"darkorange\",linetype=\"dashed\") +\n",
    "  geom_ribbon(aes(y = (pmean), ymin = plower, ymax = pupper, fill = feature), alpha = .2) +\n",
    "  xlab(\"sample size\") +\n",
    "  ylab(\"log10(p-value)\")\n",
    "\n",
    "ggplot(data = df, aes(x = n, y=pmean, group = feature)) + \n",
    "  geom_line(aes(x = n, y = pmean, color = feature), size = 1) +\n",
    "  geom_hline(yintercept=c(-2,-3), color=\"darkorange\",linetype=\"dashed\") +\n",
    "  geom_ribbon(aes(y = (pmean), ymin = plower, ymax = pupper, fill = feature), alpha = .2) +\n",
    "  xlab(\"sample size\") +\n",
    "  ylab(\"log10(p-value)\") +\n",
    "  coord_cartesian(xlim = c(1, 5000), ylim=c(-10,0))\n",
    "\n",
    "\n",
    "ggplot(data = df, aes(x = n, y=cmean, group = feature)) + \n",
    "  geom_line(aes(x = n, y = cmean, color = feature), size = 1) +\n",
    "  geom_hline(yintercept=0, color=\"darkorange\",linetype=\"dashed\") +\n",
    "  geom_ribbon(aes(y = (cmean), ymin = clower, ymax = cupper, fill = feature), alpha = .2) +\n",
    "  xlab(\"sample size\") +\n",
    "  ylab(\"Coefficient value\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4560a2e",
   "metadata": {},
   "source": [
    "Now you can trace when coefficient \"become\" significant - here you see that 'bedrooms' need  5000+ observations and 'condition' around 1000 whereas 'grade' and 'sqft_living' enter the model as significant after about 100 observations!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "dbe3abd2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ sqft_living + bedrooms + condition + grade, \n",
       "    data = kc5)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.51108 -0.10571  0.00238  0.09917  0.60312 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  5.666588   0.001018 5564.23   <2e-16 ***\n",
       "sqft_living  0.094402   0.001911   49.40   <2e-16 ***\n",
       "bedrooms    -0.015308   0.001330  -11.51   <2e-16 ***\n",
       "condition    0.028861   0.001034   27.91   <2e-16 ***\n",
       "grade        0.098832   0.001625   60.80   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1497 on 21607 degrees of freedom\n",
       "Multiple R-squared:  0.5717,\tAdjusted R-squared:  0.5716 \n",
       "F-statistic:  7210 on 4 and 21607 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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86aZNxP3PTPgcyG3jESdrF505fqvwlH9wDJi5XaJO/CE5XsGSJr16HpS9UfmHIu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\n1eCRa45qJle9mmz6+8ERtTTgBF1t9zDYh+fa4ccbV3xKL+S8Bj5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X/q2NQ3NIgSSfELrk2rnWrUV23ZHo3jiqGSOdFZAGiU7kq2NeIudj\nWmTcrCHeDbk0H5hDDKQk4WROcL/Pf/nJ/h25t+ejfRY1wVycZYGEYX2rtoOlHUh406JZcGT2\n226e+AglgiQaI6WJ9OvgCPcmx1BuWEj+4dz1nC07kQMSGJnzlIqRTHgMK8qfUzxspNcZ4HP1\n+BYlRDCrNaHIaiQF0u5yg6U85/YEJO/jmGXG0cQgsZs8LX05EpGxyYImYk9bAE4CslnXUBT0\nlHrBb4KeLOpqjGTQNjQXZBfmSyBNsDzNDJKhVzznhqe6IGLaR9MAzj5sbxuQLtcbXygLQKJ3\n2OzgGD57EgPGMzdwBM0LEp28buhswFRV+0ac/0LOzDu//OlQNUZaN6q4dtseZy5jV+uttpOu\npcZTIygHJHbBbdJ2uDBgmpkOWrM4ibziHnZm44NE16SEpi/ahmy4YXLL38lZAXidGw2k359y\n77JAElJJhdu4INSUqzJALogsi6QvpHvgd7kdSGigMhXFSPbVTh5rgcuWGCxG+v2bQ/TQbUBy\nfng7GcPThtT9hf2qnT0dMgpVcL+TQPLXaXTrXK9CpjEn1B9+2FAhhFblgbRYp7hXpSCxdYgM\nmAAiSbJzwr7l6YTAZTd3OowB0hXDGvCHxNXAzeSqHmrR2SmO0Kq8GMn+X6bSGInkG9BpoDO7\njQhIbpftjMzcmA8kZiBqB5v99psRmlI1dIbQqhyQqgzShWJ4K8LOWvvDdiuXiXw5msD1zwRm\nTCtD9XLtnEXopluLwyDRh+YHUhpCq+YDCVvmG/vxa6zVRG5C9AWpQmb14hf7nF22161b7pW2\nMhhIVxBaNR1IGHrwDTtvWsZIOE2MmyAuv5vu2sEZbh3nV7FrZ6jfhibbtwIJdmih6witmi5G\ncvx47tz+vk5dWU6Ag+RlpRLO8fyaNClIhuVV6VUu1AxgArTRqfnKRWhVFkgRa9RrmxfapjEB\nehsCd9VrIpv7duzY/dEcb9QKhwfmGUo6s5pzH8mlgthDieHe2vaak1SG0Ko8kGSUGSO5qxfe\n52OZ6MZJO9uyIRjjLa1kK4iDJO81XP9i37Zk26Gyi3jYLCR4qk2SGxgJhLY6L7R+vYxU27wf\nOG/Z3Ql8PqgVSG7xMwbvmOBkST6/OiBViWOzjET9tiO824G02EUOIVdp4pGjgLR7NSSQlSDk\nwixxr9S3s++MQdohvjpViZFGAok4ukdXmOTA8sCWaaf0QEga1mlBImZH/6rhI6s4TcDRSxw7\nvLBaj+/odE8nxhgg5X4fiYRrzmTBtiDMmXd82WnZdWgEkKQ6kVkNj0bcT/TAG8rgP4SIJRoI\n9QVmmzRGwgQDxossoow0GMqN0+PPbbmvYtXmzBUORqzR9CPdioSWatW23xNni21cXIzUMv9t\nGMgAjiZrnX4g1cisXrcQWopmNlPTMLQH/lX8oPxuxfr9mwdEEit1sNXEIzu2fVAcnQc2dM1k\nHMZA8w+w72NjkGSUDZJ/TSEm4V45/RnvQTpI9PNIRuGouVzdCiT0HRqKTy+3Stl4wDg/tKWh\nKsSxWelvY9x9pK1GwFf/30EPPN/uZEGSzGsn6h4gbZO41Yrkt2J2u8lEIR1saKhBQGKmIlXa\nG0zGEUbWnJPkwrEp18R280V8YpDsiJCB2qZwxoAXylCacKhxxNu7dhVAuh4jUQO5+bO9jYJ0\nERwqZKgNR7RjM4NErvYG16Oi4b40NfiGYR/gZZdOkqYxktBoSYDkLOXqJHGSZ510WwGdksSV\nA/mpGm7fePgnFhsFJN9OYJeBdr4dOHxCDRrjrrngzrTpiuT6UqQC187dXtuRRNOuJjgjE/qN\npVqHQ6R9n/+kcoOA5K/cNqBlg9dKsfbccgTWlylYI5o7/MGms2KkzRjWWt5V0L6je1NBusIQ\n1FijCkHiFhLoSVahnd1PJra4fH/O7TZ8coBNORRYawyQylw7l3A5O5vEi86SVEgzTZ2oSWBF\nKvRUeDVZhXhf7HhZN6+VIjQR2+K7ImNNDhJBaV9nqM3ziw4uREmxVPKR11QcI12HMN6RTek+\nbgAkfy43TTcY8g/sjRPbNwDs8PwrUrZrt5kpGaQjkYcUkteZWiAVZ+0qgHQBpV2MhKmGxuuR\nnR/bTzDkhZwgwvV8MZJLN+Dq7dV5TStBaGBIvDhVA2nfSNKRdUGyZkrpCPjve2jn1zkXkxto\n+7DAXmOAlGdpenUrilaoM3exijox0r6NxCMbxEhZWUz67GgP0ea3MbOXzOVlnULB8802VDMV\ngkRSDN496mtyF9ksU2a2eqmJ9COBbkt0LVTD1V+CBD0cOjtL7E+vebZmgwsOmoHEO1MkqRip\noCehX1bf8dISUR5IiQVODBj55AJK2/XfzurmPLl8IW2d5nLcndnY6R5Z6NhQCWUkvYb8GAno\n0nRF0V9W/0wgnScGox8kR0umv2O3ifp2zAl2rB+dw/l5XlSVOLbAPOg8JHbo6LfVJ1fSUtmu\n3VlJCG4mt52Ekg1IoCdObjEKzJVtPTpbldNtmapxQHLeLRyuSu6Tk6cV4HzydVBusgHOihaC\nlLQsjwDE0wAAF8tJREFUYWRfjoOcdqcORxfQiUAqjZE282xGMp5h1rFMeORnUN8uByQg/1Iq\nzgPJJLDkeuKudxKjfX1muLfeRfzkPGuBNESMFDQXmz50TiV+B+LZQCqJkYhOUAK8FzrOsrTv\n4ZmZKsRIecH9SdMi1rEZTLYq2d9LkkDJ04GUnbXzlJJ52JrplAZnOkcHu+xtHBybUF8lFYIU\nLmMQJKArURpISZee9qoWI0m2neThQcdbSoZvJJzZpdkwBkjZfx/JfxRynTyPmn+7J7gJXQlX\n6EpnW6AskCrekI0otizZcTFuVeogPzpLddZSDZDr2gkQKBEjhcqZZUzpjWqARE9nTOWB1Lrt\nh0Io+Zex7VKXOeBFMnRLACTYPZJ1TTW8hkLDbG8/d2wrUciTgxGXmwS1AIkXpEa9pthdbqCv\nc/h2pyD5Ka2rkrq6iycbfrNf8jPtArRTbrLhWtnStlGcJTsdcTgkRjpX5HZswiXiZAZx0MYA\nKeNXFrtNgwjxdAxMugDtlAWSzTc1a5vK+92zxma+jUs49FfCyR8edAuQNtnfGPybWOcu+Djl\nrUg0SGzRtif2RWMy26DnY3f0+isUmpQs/b1jpN9OLhmzVhLvGcwLWK5rJ+5/X9V2A4+G5NAr\n0RD4JSj8RPGpzUu2KYmRTFpmNdxfrx+7o+Mi+PBUpsE0EEnPhRqblaTsGEngultYnv6Rjq3C\nXvKb9uafYYFconEKs3ZpjZy2EHXtfocVto6hPEUTLacZmJFVkGw4vt75lixqO1re+y3P2yxu\npP065M7Xzh7D50feKdeaWxDcjB1CQYogEzWQwVB28/BCS/SzgnRSNi1zVaK1PP1NtZ1k7GzB\nHcT9BXy4jK5UcHwZCn0rVF5RkNyp/fjxSRD+e7x//Pv9220f/tvKGFvPto37vPqXNsx+3wT/\nckC6PkyZBySVh23a8UndWt4TMWs4DWC/LbWZD+g1KHz6oW+0ZWbtToteW5GQr6TViNvCXmrI\neQfWn2eLkaTqFkkpbeMRddCbCW/F7tCxUbazYdiJOfhS6HXTsJaODHh8WMC1u2pnagzwEd+t\nhOmnOJYug0QD62Ztx/tEOmU6w+Q9VkHCJLD5xPjV+PALbVkrUtItCuxsQtMbSBdMzFxduy7x\nmjNWpKPu9lPNFUmu7fOK7Lj9pm5eU9HkLt6+B+vl8aQvmUS/Q75cuaHApM7L83rcm9Qsg7UI\n2eAU0S56baX4MQOSNDlIOD3dwPVy8/b0IkbWvWOuVApB+YbalkN5kHLtEjgR8KZUEkhptLXX\nddeO2qhV20c1bBd8ewNy61pTmCzGq0MFLixgprIGw/v9NQ1llz7BMcr6G7LcArbScLeeCyRX\nSCRXIFABuk7b0OFmp5jJ+jDrGxJhX1iDig0F3s9cFYLkjII+w4FzluK13QmkCoNUUgFOWjuP\n6bv4/XZpGba1hfskC3JtEZI1VL58167IQi5/FyMJzpfQG8VIo4AELjG1RSKRoT56fkVQXvvG\nNVw4/PODZNMuzgzZS9KNsnaDgIRhPC5KXlziqyZPeKNoW4ucG2f3FAz/1ZLE0x3DtbMDEwMJ\naK5+REzONW+MtOWl7A+XfD4b1Wo8YfrdVr5Le3cxlFTTmSBRlxd9O2CEA/n3VCDZOLpZ2/HS\n5Dkcb9jOdPjA8nWhFwfWOCSHWGisMUDKc+3YLWrn/dKaac7Ib3Ia5YHUuu146e16v43SFZB8\nAnJmCex4tF6cDdq2Ky141+C6hqL9y2400HSmiTbDgHOAsTbSBl+WplNJjNSu7Whx69ltowI5\nJK26RtPv3/6CZicG//oaWTEbJxvk3e/CX1nsIlp2ieFdhSETCSmaGCSMXg2ZwGU6pun3Hh86\nUUiERq62eKc4dMKJ8ybDUBUSQnkgkYsbWgU9X0LSrABZzQySq8OtBwL6HdX5lCFvtv6RSbM7\n4dQJNAZIpdbF0Bqof2crLuxndxVk7Rq2fVIJeT5IBKVikWsvjY9g3/UkK0wNktltGhIwTQ+Q\nVdaKhIZp1fZhLbYfWcMsLxoWsTfBBakWSIPFSIZtGMzRlSVhRtK8WbtQdX0XJOMFA+4bFCbo\nvVQFSf4WRdnv/l7dhS1iopeY+cOjRXcCqbMwz4COpokQRA1QKUaSklCMRItapNYad41MqrwY\nCU3SqO2EuqRSDQUiIZpB3y58muBCqDqGqpIQyjSKb51tsNYaJTvbU5lZO5EVWdB+NO3cVia8\nbXCmBDm6dvZjgJSf/mab7iqC1T85SLIZodKaMLuaM9qSIneTjk/8gumzLCIim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bodSNmNsmufiBQkBak/SAUIZnUX4o3mSkFSkLqDFLFW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\nLqQQXFtnuQ0AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#########\n",
    "mm<-lm(price~sqft_living+bedrooms+condition+grade,data=kc5)\n",
    "par(mfrow=c(2,2))\n",
    "plot(mm)\n",
    "summary(mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "a98fe85f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ sqft_living + bedrooms + condition + grade, \n",
       "    data = kc2, subset = sample(seq(1, 21000), 150))\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.38281 -0.10708  0.01146  0.11468  0.38805 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  4.918e+00  1.394e-01  35.275  < 2e-16 ***\n",
       "sqft_living  1.589e-04  3.001e-05   5.296 4.31e-07 ***\n",
       "bedrooms    -1.458e-02  1.783e-02  -0.818  0.41492    \n",
       "condition    3.577e-02  2.189e-02   1.634  0.10433    \n",
       "grade        4.763e-02  1.741e-02   2.735  0.00701 ** \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1647 on 145 degrees of freedom\n",
       "Multiple R-squared:  0.5562,\tAdjusted R-squared:  0.5439 \n",
       "F-statistic: 45.43 on 4 and 145 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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oswGNTMSAPWseNRq6MBpmtSEl3hK/Nb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",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare fit with a smaller sample size\n",
    "mm<-lm(price~sqft_living+bedrooms+condition+grade,data=kc2,\n",
    "       subset=sample(seq(1,21000),150))\n",
    "par(mfrow=c(2,2))\n",
    "plot(mm)\n",
    "summary(mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "0804824e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = price ~ sqft_living + bedrooms + condition + grade, \n",
       "    data = kc2, subset = sample(seq(1, 21000), 1500))\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.46710 -0.11034  0.00268  0.09924  0.59487 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  4.609e+00  4.280e-02 107.672  < 2e-16 ***\n",
       "sqft_living  9.051e-05  7.640e-06  11.846  < 2e-16 ***\n",
       "bedrooms    -6.395e-03  5.391e-03  -1.186    0.236    \n",
       "condition    4.281e-02  6.005e-03   7.130 1.56e-12 ***\n",
       "grade        9.707e-02  5.288e-03  18.358  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1506 on 1495 degrees of freedom\n",
       "Multiple R-squared:  0.5899,\tAdjusted R-squared:  0.5888 \n",
       "F-statistic: 537.7 on 4 and 1495 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4oa0w4KxTqHz5EyKPkwyfmKxj0PGumwtcgETmTr5f2XJusZrmCWltMwkEzyZWuN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epHK9YkXLG94nQUtJ9252XO6KCxnpL9mgOkzo8IMTYy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\nAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare fit with a smaller sample size\n",
    "mm<-lm(price~sqft_living+bedrooms+condition+grade,data=kc2,\n",
    "       subset=sample(seq(1,21000),1500))\n",
    "par(mfrow=c(2,2))\n",
    "plot(mm)\n",
    "summary(mm)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R 4.1.2",
   "language": "R",
   "name": "ir41"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}