{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wczytywanie danych"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>familyID</th><th scope=col>individualID</th><th scope=col>IDFather</th><th scope=col>IDMother</th><th scope=col>sex</th><th scope=col>age</th><th scope=col>ethnicity</th><th scope=col>alcoholDependence</th><th scope=col>AgeOnset</th><th scope=col>MaxDinks</th><th scope=col>packsDay</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>10084   </td><td>10000089</td><td>10000526</td><td>10000031</td><td>F       </td><td>30      </td><td>6       </td><td>5       </td><td>16      </td><td>24      </td><td>17.00   </td></tr>\n",
       "\t<tr><td>10084   </td><td>10000758</td><td>10000526</td><td>10000031</td><td>F       </td><td>31      </td><td>6       </td><td>5       </td><td>30      </td><td>12      </td><td>16.00   </td></tr>\n",
       "\t<tr><td>10084   </td><td>10001094</td><td>       0</td><td>       0</td><td>M       </td><td> 0      </td><td>0       </td><td>0       </td><td> 0      </td><td>-9      </td><td>-9.00   </td></tr>\n",
       "\t<tr><td>10084   </td><td>10000133</td><td>10001094</td><td>10000758</td><td>M       </td><td>18      </td><td>6       </td><td>3       </td><td> 0      </td><td>18      </td><td> 0.45   </td></tr>\n",
       "\t<tr><td>10084   </td><td>10001039</td><td>10000526</td><td>10000031</td><td>M       </td><td>28      </td><td>6       </td><td>5       </td><td>16      </td><td>40      </td><td> 0.00   </td></tr>\n",
       "\t<tr><td>10084   </td><td>10000194</td><td>10000526</td><td>10000031</td><td>F       </td><td>24      </td><td>6       </td><td>3       </td><td> 0      </td><td>20      </td><td> 8.00   </td></tr>\n",
       "\t<tr><td>10084   </td><td>10000526</td><td>       0</td><td>       0</td><td>M       </td><td>60      </td><td>6       </td><td>5       </td><td>38      </td><td>24      </td><td>42.00   </td></tr>\n",
       "\t<tr><td>10084   </td><td>10000031</td><td>       0</td><td>       0</td><td>F       </td><td>60      </td><td>6       </td><td>3       </td><td> 0      </td><td> 7      </td><td>58.50   </td></tr>\n",
       "\t<tr><td>10130   </td><td>10001565</td><td>10001436</td><td>10001364</td><td>F       </td><td>38      </td><td>6       </td><td>5       </td><td>18      </td><td>75      </td><td>30.00   </td></tr>\n",
       "\t<tr><td>10130   </td><td>10000919</td><td>10001436</td><td>10001364</td><td>M       </td><td>40      </td><td>6       </td><td>5       </td><td>33      </td><td>48      </td><td> 0.00   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " familyID & individualID & IDFather & IDMother & sex & age & ethnicity & alcoholDependence & AgeOnset & MaxDinks & packsDay\\\\\n",
       "\\hline\n",
       "\t 10084    & 10000089 & 10000526 & 10000031 & F        & 30       & 6        & 5        & 16       & 24       & 17.00   \\\\\n",
       "\t 10084    & 10000758 & 10000526 & 10000031 & F        & 31       & 6        & 5        & 30       & 12       & 16.00   \\\\\n",
       "\t 10084    & 10001094 &        0 &        0 & M        &  0       & 0        & 0        &  0       & -9       & -9.00   \\\\\n",
       "\t 10084    & 10000133 & 10001094 & 10000758 & M        & 18       & 6        & 3        &  0       & 18       &  0.45   \\\\\n",
       "\t 10084    & 10001039 & 10000526 & 10000031 & M        & 28       & 6        & 5        & 16       & 40       &  0.00   \\\\\n",
       "\t 10084    & 10000194 & 10000526 & 10000031 & F        & 24       & 6        & 3        &  0       & 20       &  8.00   \\\\\n",
       "\t 10084    & 10000526 &        0 &        0 & M        & 60       & 6        & 5        & 38       & 24       & 42.00   \\\\\n",
       "\t 10084    & 10000031 &        0 &        0 & F        & 60       & 6        & 3        &  0       &  7       & 58.50   \\\\\n",
       "\t 10130    & 10001565 & 10001436 & 10001364 & F        & 38       & 6        & 5        & 18       & 75       & 30.00   \\\\\n",
       "\t 10130    & 10000919 & 10001436 & 10001364 & M        & 40       & 6        & 5        & 33       & 48       &  0.00   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| familyID | individualID | IDFather | IDMother | sex | age | ethnicity | alcoholDependence | AgeOnset | MaxDinks | packsDay |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 10084    | 10000089 | 10000526 | 10000031 | F        | 30       | 6        | 5        | 16       | 24       | 17.00    |\n",
       "| 10084    | 10000758 | 10000526 | 10000031 | F        | 31       | 6        | 5        | 30       | 12       | 16.00    |\n",
       "| 10084    | 10001094 |        0 |        0 | M        |  0       | 0        | 0        |  0       | -9       | -9.00    |\n",
       "| 10084    | 10000133 | 10001094 | 10000758 | M        | 18       | 6        | 3        |  0       | 18       |  0.45    |\n",
       "| 10084    | 10001039 | 10000526 | 10000031 | M        | 28       | 6        | 5        | 16       | 40       |  0.00    |\n",
       "| 10084    | 10000194 | 10000526 | 10000031 | F        | 24       | 6        | 3        |  0       | 20       |  8.00    |\n",
       "| 10084    | 10000526 |        0 |        0 | M        | 60       | 6        | 5        | 38       | 24       | 42.00    |\n",
       "| 10084    | 10000031 |        0 |        0 | F        | 60       | 6        | 3        |  0       |  7       | 58.50    |\n",
       "| 10130    | 10001565 | 10001436 | 10001364 | F        | 38       | 6        | 5        | 18       | 75       | 30.00    |\n",
       "| 10130    | 10000919 | 10001436 | 10001364 | M        | 40       | 6        | 5        | 33       | 48       |  0.00    |\n",
       "\n"
      ],
      "text/plain": [
       "   familyID individualID IDFather IDMother sex age ethnicity alcoholDependence\n",
       "1  10084    10000089     10000526 10000031 F   30  6         5                \n",
       "2  10084    10000758     10000526 10000031 F   31  6         5                \n",
       "3  10084    10001094            0        0 M    0  0         0                \n",
       "4  10084    10000133     10001094 10000758 M   18  6         3                \n",
       "5  10084    10001039     10000526 10000031 M   28  6         5                \n",
       "6  10084    10000194     10000526 10000031 F   24  6         3                \n",
       "7  10084    10000526            0        0 M   60  6         5                \n",
       "8  10084    10000031            0        0 F   60  6         3                \n",
       "9  10130    10001565     10001436 10001364 F   38  6         5                \n",
       "10 10130    10000919     10001436 10001364 M   40  6         5                \n",
       "   AgeOnset MaxDinks packsDay\n",
       "1  16       24       17.00   \n",
       "2  30       12       16.00   \n",
       "3   0       -9       -9.00   \n",
       "4   0       18        0.45   \n",
       "5  16       40        0.00   \n",
       "6   0       20        8.00   \n",
       "7  38       24       42.00   \n",
       "8   0        7       58.50   \n",
       "9  18       75       30.00   \n",
       "10 33       48        0.00   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaw = read.table('http://theta.edu.pl/wp-content/uploads/2019/12/gaw.csv', header = TRUE, sep = ';', dec = ',')\n",
    "head(gaw, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eksploracja danych"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "    familyID      individualID      IDFather           IDMother        sex    \n",
       " Min.   :10001   Min.   :1e+07   Min.   :       0   Min.   :       0   F:788  \n",
       " 1st Qu.:10033   1st Qu.:1e+07   1st Qu.:       0   1st Qu.:       0   M:826  \n",
       " Median :10068   Median :1e+07   Median :10000446   Median :10000403          \n",
       " Mean   :10070   Mean   :1e+07   Mean   : 6871685   Mean   : 6871658          \n",
       " 3rd Qu.:10106   3rd Qu.:1e+07   3rd Qu.:10001052   3rd Qu.:10001005          \n",
       " Max.   :10143   Max.   :1e+07   Max.   :10001609   Max.   :10001607          \n",
       "      age          ethnicity     alcoholDependence    AgeOnset     \n",
       " Min.   : 0.00   Min.   :0.000   Min.   :0.000     Min.   : 0.000  \n",
       " 1st Qu.:23.00   1st Qu.:4.000   1st Qu.:1.000     1st Qu.: 0.000  \n",
       " Median :34.00   Median :6.000   Median :3.000     Median : 0.000  \n",
       " Mean   :34.48   Mean   :4.922   Mean   :3.006     Mean   : 8.769  \n",
       " 3rd Qu.:47.00   3rd Qu.:6.000   3rd Qu.:5.000     3rd Qu.:18.000  \n",
       " Max.   :91.00   Max.   :8.000   Max.   :5.000     Max.   :66.000  \n",
       "    MaxDinks        packsDay      \n",
       " Min.   :-9.00   Min.   : -9.000  \n",
       " 1st Qu.: 3.00   1st Qu.:  0.000  \n",
       " Median :10.00   Median :  1.587  \n",
       " Mean   :13.71   Mean   : 11.674  \n",
       " 3rd Qu.:22.75   3rd Qu.: 18.000  \n",
       " Max.   :96.00   Max.   :193.000  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(gaw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "FALSE  TRUE \n",
       "  226  1388 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(gaw$age != 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "    familyID      individualID      IDFather           IDMother        sex    \n",
       " Min.   :10001   Min.   :1e+07   Min.   :       0   Min.   :       0   F:718  \n",
       " 1st Qu.:10033   1st Qu.:1e+07   1st Qu.:10000090   1st Qu.:10000073   M:663  \n",
       " Median :10069   Median :1e+07   Median :10000620   Median :10000527          \n",
       " Mean   :10070   Mean   :1e+07   Mean   : 7900715   Mean   : 7900683          \n",
       " 3rd Qu.:10106   3rd Qu.:1e+07   3rd Qu.:10001122   3rd Qu.:10001083          \n",
       " Max.   :10143   Max.   :1e+07   Max.   :10001609   Max.   :10001607          \n",
       "      age          ethnicity     alcoholDependence    AgeOnset    \n",
       " Min.   :17.00   Min.   :0.000   Min.   :1.000     Min.   : 0.00  \n",
       " 1st Qu.:29.00   1st Qu.:6.000   1st Qu.:3.000     1st Qu.: 0.00  \n",
       " Median :37.00   Median :6.000   Median :3.000     Median : 0.00  \n",
       " Mean   :40.04   Mean   :5.728   Mean   :3.495     Mean   :10.17  \n",
       " 3rd Qu.:51.00   3rd Qu.:6.000   3rd Qu.:5.000     3rd Qu.:19.00  \n",
       " Max.   :91.00   Max.   :8.000   Max.   :5.000     Max.   :66.00  \n",
       "    MaxDinks        packsDay     \n",
       " Min.   : 0.00   Min.   :  0.00  \n",
       " 1st Qu.: 6.00   1st Qu.:  0.00  \n",
       " Median :12.00   Median :  5.25  \n",
       " Mean   :17.43   Mean   : 15.16  \n",
       " 3rd Qu.:24.00   3rd Qu.: 21.00  \n",
       " Max.   :96.00   Max.   :193.00  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaw = gaw[gaw$age != 0, ]\n",
    "gaw = gaw[gaw$packsDay != -9, ]\n",
    "summary(gaw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#install.packages(\"psych\")\n",
    "library(psych)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>vars</th><th scope=col>n</th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>median</th><th scope=col>trimmed</th><th scope=col>mad</th><th scope=col>min</th><th scope=col>max</th><th scope=col>range</th><th scope=col>skew</th><th scope=col>kurtosis</th><th scope=col>se</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>familyID</th><td> 1          </td><td>1381        </td><td>1.007027e+04</td><td>4.193776e+01</td><td>   10069.00 </td><td>1.006995e+04</td><td> 54.85620   </td><td>   10001    </td><td>   10143    </td><td>     142    </td><td> 0.05270503 </td><td>-1.26045317 </td><td>1.128518e+00</td></tr>\n",
       "\t<tr><th scope=row>individualID</th><td> 2          </td><td>1381        </td><td>1.000081e+07</td><td>4.660408e+02</td><td>10000814.00 </td><td>1.000081e+07</td><td>596.00520   </td><td>10000001    </td><td>10001614    </td><td>    1613    </td><td>-0.01373681 </td><td>-1.18923885 </td><td>1.254085e+01</td></tr>\n",
       "\t<tr><th scope=row>IDFather</th><td> 3          </td><td>1381        </td><td>7.900715e+06</td><td>4.074838e+06</td><td>10000620.00 </td><td>8.625049e+06</td><td>765.02160   </td><td>       0    </td><td>10001609    </td><td>10001609    </td><td>-1.42249007 </td><td> 0.02349663 </td><td>1.096512e+05</td></tr>\n",
       "\t<tr><th scope=row>IDMother</th><td> 4          </td><td>1381        </td><td>7.900683e+06</td><td>4.074821e+06</td><td>10000527.00 </td><td>8.625010e+06</td><td>735.36960   </td><td>       0    </td><td>10001607    </td><td>10001607    </td><td>-1.42249006 </td><td> 0.02349663 </td><td>1.096508e+05</td></tr>\n",
       "\t<tr><th scope=row>sex*</th><td> 5          </td><td>1381        </td><td>1.480087e+00</td><td>4.997843e-01</td><td>       1.00 </td><td>1.475113e+00</td><td>  0.00000   </td><td>       1    </td><td>       2    </td><td>       1    </td><td> 0.07962910 </td><td>-1.99510231 </td><td>1.344887e-02</td></tr>\n",
       "\t<tr><th scope=row>age</th><td> 6          </td><td>1381        </td><td>4.004055e+01</td><td>1.519329e+01</td><td>      37.00 </td><td>3.897919e+01</td><td> 14.82600   </td><td>      17    </td><td>      91    </td><td>      74    </td><td> 0.63399149 </td><td>-0.39609744 </td><td>4.088415e-01</td></tr>\n",
       "\t<tr><th scope=row>ethnicity</th><td> 7          </td><td>1381        </td><td>5.727734e+00</td><td>9.346889e-01</td><td>       6.00 </td><td>5.860633e+00</td><td>  0.00000   </td><td>       0    </td><td>       8    </td><td>       8    </td><td>-2.11702045 </td><td> 7.05280083 </td><td>2.515187e-02</td></tr>\n",
       "\t<tr><th scope=row>alcoholDependence</th><td> 8          </td><td>1381        </td><td>3.494569e+00</td><td>1.564833e+00</td><td>       3.00 </td><td>3.618100e+00</td><td>  2.96520   </td><td>       1    </td><td>       5    </td><td>       4    </td><td>-0.44632263 </td><td>-1.25963346 </td><td>4.210863e-02</td></tr>\n",
       "\t<tr><th scope=row>AgeOnset</th><td> 9          </td><td>1381        </td><td>1.017161e+01</td><td>1.254696e+01</td><td>       0.00 </td><td>8.334842e+00</td><td>  0.00000   </td><td>       0    </td><td>      66    </td><td>      66    </td><td> 0.98619854 </td><td> 0.50232360 </td><td>3.376306e-01</td></tr>\n",
       "\t<tr><th scope=row>MaxDinks</th><td>10          </td><td>1381        </td><td>1.743012e+01</td><td>1.605756e+01</td><td>      12.00 </td><td>1.474389e+01</td><td> 11.86080   </td><td>       0    </td><td>      96    </td><td>      96    </td><td> 1.89569945 </td><td> 4.72287697 </td><td>4.320985e-01</td></tr>\n",
       "\t<tr><th scope=row>packsDay</th><td>11          </td><td>1381        </td><td>1.516225e+01</td><td>2.301009e+01</td><td>       5.25 </td><td>1.018169e+01</td><td>  7.78365   </td><td>       0    </td><td>     193    </td><td>     193    </td><td> 2.60677859 </td><td> 9.69008086 </td><td>6.191864e-01</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllllll}\n",
       "  & vars & n & mean & sd & median & trimmed & mad & min & max & range & skew & kurtosis & se\\\\\n",
       "\\hline\n",
       "\tfamilyID &  1           & 1381         & 1.007027e+04 & 4.193776e+01 &    10069.00  & 1.006995e+04 &  54.85620    &    10001     &    10143     &      142     &  0.05270503  & -1.26045317  & 1.128518e+00\\\\\n",
       "\tindividualID &  2           & 1381         & 1.000081e+07 & 4.660408e+02 & 10000814.00  & 1.000081e+07 & 596.00520    & 10000001     & 10001614     &     1613     & -0.01373681  & -1.18923885  & 1.254085e+01\\\\\n",
       "\tIDFather &  3           & 1381         & 7.900715e+06 & 4.074838e+06 & 10000620.00  & 8.625049e+06 & 765.02160    &        0     & 10001609     & 10001609     & -1.42249007  &  0.02349663  & 1.096512e+05\\\\\n",
       "\tIDMother &  4           & 1381         & 7.900683e+06 & 4.074821e+06 & 10000527.00  & 8.625010e+06 & 735.36960    &        0     & 10001607     & 10001607     & -1.42249006  &  0.02349663  & 1.096508e+05\\\\\n",
       "\tsex* &  5           & 1381         & 1.480087e+00 & 4.997843e-01 &        1.00  & 1.475113e+00 &   0.00000    &        1     &        2     &        1     &  0.07962910  & -1.99510231  & 1.344887e-02\\\\\n",
       "\tage &  6           & 1381         & 4.004055e+01 & 1.519329e+01 &       37.00  & 3.897919e+01 &  14.82600    &       17     &       91     &       74     &  0.63399149  & -0.39609744  & 4.088415e-01\\\\\n",
       "\tethnicity &  7           & 1381         & 5.727734e+00 & 9.346889e-01 &        6.00  & 5.860633e+00 &   0.00000    &        0     &        8     &        8     & -2.11702045  &  7.05280083  & 2.515187e-02\\\\\n",
       "\talcoholDependence &  8           & 1381         & 3.494569e+00 & 1.564833e+00 &        3.00  & 3.618100e+00 &   2.96520    &        1     &        5     &        4     & -0.44632263  & -1.25963346  & 4.210863e-02\\\\\n",
       "\tAgeOnset &  9           & 1381         & 1.017161e+01 & 1.254696e+01 &        0.00  & 8.334842e+00 &   0.00000    &        0     &       66     &       66     &  0.98619854  &  0.50232360  & 3.376306e-01\\\\\n",
       "\tMaxDinks & 10           & 1381         & 1.743012e+01 & 1.605756e+01 &       12.00  & 1.474389e+01 &  11.86080    &        0     &       96     &       96     &  1.89569945  &  4.72287697  & 4.320985e-01\\\\\n",
       "\tpacksDay & 11           & 1381         & 1.516225e+01 & 2.301009e+01 &        5.25  & 1.018169e+01 &   7.78365    &        0     &      193     &      193     &  2.60677859  &  9.69008086  & 6.191864e-01\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| familyID |  1           | 1381         | 1.007027e+04 | 4.193776e+01 |    10069.00  | 1.006995e+04 |  54.85620    |    10001     |    10143     |      142     |  0.05270503  | -1.26045317  | 1.128518e+00 |\n",
       "| individualID |  2           | 1381         | 1.000081e+07 | 4.660408e+02 | 10000814.00  | 1.000081e+07 | 596.00520    | 10000001     | 10001614     |     1613     | -0.01373681  | -1.18923885  | 1.254085e+01 |\n",
       "| IDFather |  3           | 1381         | 7.900715e+06 | 4.074838e+06 | 10000620.00  | 8.625049e+06 | 765.02160    |        0     | 10001609     | 10001609     | -1.42249007  |  0.02349663  | 1.096512e+05 |\n",
       "| IDMother |  4           | 1381         | 7.900683e+06 | 4.074821e+06 | 10000527.00  | 8.625010e+06 | 735.36960    |        0     | 10001607     | 10001607     | -1.42249006  |  0.02349663  | 1.096508e+05 |\n",
       "| sex* |  5           | 1381         | 1.480087e+00 | 4.997843e-01 |        1.00  | 1.475113e+00 |   0.00000    |        1     |        2     |        1     |  0.07962910  | -1.99510231  | 1.344887e-02 |\n",
       "| age |  6           | 1381         | 4.004055e+01 | 1.519329e+01 |       37.00  | 3.897919e+01 |  14.82600    |       17     |       91     |       74     |  0.63399149  | -0.39609744  | 4.088415e-01 |\n",
       "| ethnicity |  7           | 1381         | 5.727734e+00 | 9.346889e-01 |        6.00  | 5.860633e+00 |   0.00000    |        0     |        8     |        8     | -2.11702045  |  7.05280083  | 2.515187e-02 |\n",
       "| alcoholDependence |  8           | 1381         | 3.494569e+00 | 1.564833e+00 |        3.00  | 3.618100e+00 |   2.96520    |        1     |        5     |        4     | -0.44632263  | -1.25963346  | 4.210863e-02 |\n",
       "| AgeOnset |  9           | 1381         | 1.017161e+01 | 1.254696e+01 |        0.00  | 8.334842e+00 |   0.00000    |        0     |       66     |       66     |  0.98619854  |  0.50232360  | 3.376306e-01 |\n",
       "| MaxDinks | 10           | 1381         | 1.743012e+01 | 1.605756e+01 |       12.00  | 1.474389e+01 |  11.86080    |        0     |       96     |       96     |  1.89569945  |  4.72287697  | 4.320985e-01 |\n",
       "| packsDay | 11           | 1381         | 1.516225e+01 | 2.301009e+01 |        5.25  | 1.018169e+01 |   7.78365    |        0     |      193     |      193     |  2.60677859  |  9.69008086  | 6.191864e-01 |\n",
       "\n"
      ],
      "text/plain": [
       "                  vars n    mean         sd           median      trimmed     \n",
       "familyID           1   1381 1.007027e+04 4.193776e+01    10069.00 1.006995e+04\n",
       "individualID       2   1381 1.000081e+07 4.660408e+02 10000814.00 1.000081e+07\n",
       "IDFather           3   1381 7.900715e+06 4.074838e+06 10000620.00 8.625049e+06\n",
       "IDMother           4   1381 7.900683e+06 4.074821e+06 10000527.00 8.625010e+06\n",
       "sex*               5   1381 1.480087e+00 4.997843e-01        1.00 1.475113e+00\n",
       "age                6   1381 4.004055e+01 1.519329e+01       37.00 3.897919e+01\n",
       "ethnicity          7   1381 5.727734e+00 9.346889e-01        6.00 5.860633e+00\n",
       "alcoholDependence  8   1381 3.494569e+00 1.564833e+00        3.00 3.618100e+00\n",
       "AgeOnset           9   1381 1.017161e+01 1.254696e+01        0.00 8.334842e+00\n",
       "MaxDinks          10   1381 1.743012e+01 1.605756e+01       12.00 1.474389e+01\n",
       "packsDay          11   1381 1.516225e+01 2.301009e+01        5.25 1.018169e+01\n",
       "                  mad       min      max      range    skew        kurtosis   \n",
       "familyID           54.85620    10001    10143      142  0.05270503 -1.26045317\n",
       "individualID      596.00520 10000001 10001614     1613 -0.01373681 -1.18923885\n",
       "IDFather          765.02160        0 10001609 10001609 -1.42249007  0.02349663\n",
       "IDMother          735.36960        0 10001607 10001607 -1.42249006  0.02349663\n",
       "sex*                0.00000        1        2        1  0.07962910 -1.99510231\n",
       "age                14.82600       17       91       74  0.63399149 -0.39609744\n",
       "ethnicity           0.00000        0        8        8 -2.11702045  7.05280083\n",
       "alcoholDependence   2.96520        1        5        4 -0.44632263 -1.25963346\n",
       "AgeOnset            0.00000        0       66       66  0.98619854  0.50232360\n",
       "MaxDinks           11.86080        0       96       96  1.89569945  4.72287697\n",
       "packsDay            7.78365        0      193      193  2.60677859  9.69008086\n",
       "                  se          \n",
       "familyID          1.128518e+00\n",
       "individualID      1.254085e+01\n",
       "IDFather          1.096512e+05\n",
       "IDMother          1.096508e+05\n",
       "sex*              1.344887e-02\n",
       "age               4.088415e-01\n",
       "ethnicity         2.515187e-02\n",
       "alcoholDependence 4.210863e-02\n",
       "AgeOnset          3.376306e-01\n",
       "MaxDinks          4.320985e-01\n",
       "packsDay          6.191864e-01"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "describe(gaw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sLH675XEXQB2nMwbPISoXCrCLoA7TkY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\nQJEAARQJEECRAAH/AM+2Jz/ZrLUvAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Histogram of gaw$age\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(gaw$age)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test Shapiro-Wilka"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  17.00   29.00   37.00   40.04   51.00   91.00 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(gaw$age)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  gaw$age\n",
       "W = 0.94605, p-value < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(gaw$age)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.634680731360363"
      ],
      "text/latex": [
       "0.634680731360363"
      ],
      "text/markdown": [
       "0.634680731360363"
      ],
      "text/plain": [
       "[1] 0.6346807"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(moments)\n",
    "skewness(gaw$age)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "-0.0160351083902215"
      ],
      "text/latex": [
       "-0.0160351083902215"
      ],
      "text/markdown": [
       "-0.0160351083902215"
      ],
      "text/plain": [
       "[1] -0.01603511"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "skewness(log(gaw$age))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IgkB5HAIpIcRAKLSHIQCSwiyZFe/nYY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\ngEgACiASgAKIBKAAIgEogEgACvwDLFzUzeAEfdIAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Histogram of log(gaw$age)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow = c(1, 2))\n",
    "hist(gaw$age)\n",
    "hist(log(gaw$age))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### regresja liniowa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = age ~ MaxDinks, data = gaw)\n",
       "\n",
       "Coefficients:\n",
       "(Intercept)     MaxDinks  \n",
       "    42.7459      -0.1552  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm(age~MaxDinks, data = gaw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>(Intercept)</dt>\n",
       "\t\t<dd>42.7458922115112</dd>\n",
       "\t<dt>MaxDinks</dt>\n",
       "\t\t<dd>-0.155210715969298</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 42.7458922115112\n",
       "\\item[MaxDinks] -0.155210715969298\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   42.7458922115112MaxDinks\n",
       ":   -0.155210715969298\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)    MaxDinks \n",
       " 42.7458922  -0.1552107 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "41.9698386316647"
      ],
      "text/latex": [
       "41.9698386316647"
      ],
      "text/markdown": [
       "41.9698386316647"
      ],
      "text/plain": [
       "[1] 41.96984"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "41.9698386316647"
      ],
      "text/latex": [
       "41.9698386316647"
      ],
      "text/markdown": [
       "41.9698386316647"
      ],
      "text/plain": [
       "[1] 41.96984"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = lm(age~MaxDinks, data = gaw)\n",
    "m$coef\n",
    "sum(m$coef*c(1, 5))\n",
    "42.7458922115112+(-0.155210715969298)*5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = age ~ MaxDinks, data = gaw)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-24.746 -11.021  -2.883  11.427  49.806 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 42.74589    0.59557  71.774  < 2e-16 ***\n",
       "MaxDinks    -0.15521    0.02513  -6.175 8.67e-10 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 14.99 on 1379 degrees of freedom\n",
       "Multiple R-squared:  0.02691,\tAdjusted R-squared:  0.0262 \n",
       "F-statistic: 38.13 on 1 and 1379 DF,  p-value: 8.674e-10\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\widehat{y} = 42.74589 - 0.15521*MaxDinks$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qLpEFfhhrvdtG1e1htm5lzfhGQF88i5AWX+rLPYLE2EpP5WuliRRubRzokzx4r0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\nARASAAZASAAYACEBYMD/sZtJ+KOJRVkAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(gaw$MaxDinks, gaw$age, lwd = 2, xlab = \"MaxDrinks\", ylab = \"Age\")\n",
    "abline(m, lwd = 2, col = \"red\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = gaw$age ~ gaw$MaxDinks)\n",
       "\n",
       "Coefficients:\n",
       " (Intercept)  gaw$MaxDinks  \n",
       "     42.7459       -0.1552  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm(gaw$age~gaw$MaxDinks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " sex          age          ethnicity     alcoholDependence    AgeOnset    \n",
       " F:718   Min.   :17.00   Min.   :0.000   Min.   :1.000     Min.   : 0.00  \n",
       " M:663   1st Qu.:29.00   1st Qu.:6.000   1st Qu.:3.000     1st Qu.: 0.00  \n",
       "         Median :37.00   Median :6.000   Median :3.000     Median : 0.00  \n",
       "         Mean   :40.04   Mean   :5.728   Mean   :3.495     Mean   :10.17  \n",
       "         3rd Qu.:51.00   3rd Qu.:6.000   3rd Qu.:5.000     3rd Qu.:19.00  \n",
       "         Max.   :91.00   Max.   :8.000   Max.   :5.000     Max.   :66.00  \n",
       "    MaxDinks        packsDay     \n",
       " Min.   : 0.00   Min.   :  0.00  \n",
       " 1st Qu.: 6.00   1st Qu.:  0.00  \n",
       " Median :12.00   Median :  5.25  \n",
       " Mean   :17.43   Mean   : 15.16  \n",
       " 3rd Qu.:24.00   3rd Qu.: 21.00  \n",
       " Max.   :96.00   Max.   :193.00  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       " sex          age          ethnicity     alcoholDependence    AgeOnset    \n",
       " F:199   Min.   :18.00   Min.   :1.000   Min.   :5         Min.   :12.00  \n",
       " M:423   1st Qu.:30.00   1st Qu.:6.000   1st Qu.:5         1st Qu.:17.00  \n",
       "         Median :35.00   Median :6.000   Median :5         Median :20.00  \n",
       "         Mean   :38.08   Mean   :5.773   Mean   :5         Mean   :22.58  \n",
       "         3rd Qu.:44.00   3rd Qu.:6.000   3rd Qu.:5         3rd Qu.:25.00  \n",
       "         Max.   :74.00   Max.   :8.000   Max.   :5         Max.   :66.00  \n",
       "    MaxDinks        packsDay      \n",
       " Min.   : 0.00   Min.   :  0.000  \n",
       " 1st Qu.:15.25   1st Qu.:  2.138  \n",
       " Median :24.00   Median : 13.291  \n",
       " Mean   :27.31   Mean   : 20.533  \n",
       " 3rd Qu.:35.00   3rd Qu.: 27.688  \n",
       " Max.   :96.00   Max.   :193.000  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>sex</th><th scope=col>age</th><th scope=col>ethnicity</th><th scope=col>AgeOnset</th><th scope=col>MaxDinks</th><th scope=col>packsDay</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>F </td><td>30</td><td>6 </td><td>16</td><td>24</td><td>17</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>F </td><td>31</td><td>6 </td><td>30</td><td>12</td><td>16</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>M </td><td>28</td><td>6 </td><td>16</td><td>40</td><td> 0</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>M </td><td>60</td><td>6 </td><td>38</td><td>24</td><td>42</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>F </td><td>38</td><td>6 </td><td>18</td><td>75</td><td>30</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>M </td><td>40</td><td>6 </td><td>33</td><td>48</td><td> 0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       "  & sex & age & ethnicity & AgeOnset & MaxDinks & packsDay\\\\\n",
       "\\hline\n",
       "\t1 & F  & 30 & 6  & 16 & 24 & 17\\\\\n",
       "\t2 & F  & 31 & 6  & 30 & 12 & 16\\\\\n",
       "\t5 & M  & 28 & 6  & 16 & 40 &  0\\\\\n",
       "\t7 & M  & 60 & 6  & 38 & 24 & 42\\\\\n",
       "\t9 & F  & 38 & 6  & 18 & 75 & 30\\\\\n",
       "\t10 & M  & 40 & 6  & 33 & 48 &  0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | sex | age | ethnicity | AgeOnset | MaxDinks | packsDay |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 1 | F  | 30 | 6  | 16 | 24 | 17 |\n",
       "| 2 | F  | 31 | 6  | 30 | 12 | 16 |\n",
       "| 5 | M  | 28 | 6  | 16 | 40 |  0 |\n",
       "| 7 | M  | 60 | 6  | 38 | 24 | 42 |\n",
       "| 9 | F  | 38 | 6  | 18 | 75 | 30 |\n",
       "| 10 | M  | 40 | 6  | 33 | 48 |  0 |\n",
       "\n"
      ],
      "text/plain": [
       "   sex age ethnicity AgeOnset MaxDinks packsDay\n",
       "1  F   30  6         16       24       17      \n",
       "2  F   31  6         30       12       16      \n",
       "5  M   28  6         16       40        0      \n",
       "7  M   60  6         38       24       42      \n",
       "9  F   38  6         18       75       30      \n",
       "10 M   40  6         33       48        0      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaw2 = gaw[, -c(1:4)]\n",
    "summary(gaw2)\n",
    "gaw2 = gaw2[gaw$AgeOnset > 0, ]\n",
    "summary(gaw2)\n",
    "gaw2 = gaw2[, -4]\n",
    "head(gaw2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = age ~ ., data = gaw2)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-33.092  -5.074  -0.663   3.734  31.776 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 17.52823    2.51814   6.961 8.69e-12 ***\n",
       "sexM         3.92909    0.74233   5.293 1.68e-07 ***\n",
       "ethnicity   -0.15644    0.37556  -0.417  0.67715    \n",
       "AgeOnset     0.69478    0.04223  16.451  < 2e-16 ***\n",
       "MaxDinks    -0.05402    0.02066  -2.615  0.00914 ** \n",
       "packsDay     0.22230    0.01393  15.963  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 8.135 on 616 degrees of freedom\n",
       "Multiple R-squared:  0.5707,\tAdjusted R-squared:  0.5672 \n",
       "F-statistic: 163.7 on 5 and 616 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2 = lm(age ~ ., data =gaw2)\n",
    "summary(model2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = age ~ . - ethnicity, data = gaw2)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-33.054  -5.098  -0.685   3.850  31.738 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 16.61395    1.23355  13.468  < 2e-16 ***\n",
       "sexM         3.92383    0.74173   5.290  1.7e-07 ***\n",
       "AgeOnset     0.69578    0.04214  16.513  < 2e-16 ***\n",
       "MaxDinks    -0.05398    0.02064  -2.615  0.00914 ** \n",
       "packsDay     0.22187    0.01388  15.988  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 8.13 on 617 degrees of freedom\n",
       "Multiple R-squared:  0.5705,\tAdjusted R-squared:  0.5677 \n",
       "F-statistic: 204.9 on 4 and 617 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2b = lm(age ~ . - ethnicity, data =gaw2)\n",
    "summary(model2b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. \n",
       "-4.304278 -0.628111 -0.084700  0.000048  0.475898  3.956511 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "\t<dt>182</dt>\n",
       "\t\t<dd>65</dd>\n",
       "\t<dt>183</dt>\n",
       "\t\t<dd>66</dd>\n",
       "\t<dt>237</dt>\n",
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       "\t<dt>784</dt>\n",
       "\t\t<dd>323</dd>\n",
       "\t<dt>786</dt>\n",
       "\t\t<dd>324</dd>\n",
       "\t<dt>800</dt>\n",
       "\t\t<dd>330</dd>\n",
       "\t<dt>814</dt>\n",
       "\t\t<dd>333</dd>\n",
       "\t<dt>821</dt>\n",
       "\t\t<dd>337</dd>\n",
       "\t<dt>940</dt>\n",
       "\t\t<dd>382</dd>\n",
       "\t<dt>992</dt>\n",
       "\t\t<dd>404</dd>\n",
       "\t<dt>1023</dt>\n",
       "\t\t<dd>412</dd>\n",
       "\t<dt>1274</dt>\n",
       "\t\t<dd>504</dd>\n",
       "\t<dt>1404</dt>\n",
       "\t\t<dd>551</dd>\n",
       "\t<dt>1425</dt>\n",
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       "\t<dt>1435</dt>\n",
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       "\t\t<dd>585</dd>\n",
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       "\t<dt>1610</dt>\n",
       "\t\t<dd>621</dd>\n",
       "</dl>\n"
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      "text/latex": [
       "\\begin{description*}\n",
       "\\item[176] 63\n",
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       "\\item[237] 84\n",
       "\\item[295] 109\n",
       "\\item[351] 128\n",
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       "\\item[625] 254\n",
       "\\item[728] 298\n",
       "\\item[731] 300\n",
       "\\item[751] 306\n",
       "\\item[784] 323\n",
       "\\item[786] 324\n",
       "\\item[800] 330\n",
       "\\item[814] 333\n",
       "\\item[821] 337\n",
       "\\item[940] 382\n",
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       "\\item[1274] 504\n",
       "\\item[1404] 551\n",
       "\\item[1425] 559\n",
       "\\item[1435] 562\n",
       "\\item[1498] 577\n",
       "\\item[1500] 578\n",
       "\\item[1522] 585\n",
       "\\item[1595] 613\n",
       "\\item[1604] 618\n",
       "\\item[1610] 621\n",
       "\\end{description*}\n"
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      "text/markdown": [
       "176\n",
       ":   63180\n",
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       ":   330814\n",
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       ":   337940\n",
       ":   382992\n",
       ":   4041023\n",
       ":   4121274\n",
       ":   5041404\n",
       ":   5511425\n",
       ":   5591435\n",
       ":   5621498\n",
       ":   5771500\n",
       ":   5781522\n",
       ":   5851595\n",
       ":   6131604\n",
       ":   6181610\n",
       ":   621\n",
       "\n"
      ],
      "text/plain": [
       " 176  180  182  183  237  295  351  612  625  728  731  751  784  786  800  814 \n",
       "  63   64   65   66   84  109  128  248  254  298  300  306  323  324  330  333 \n",
       " 821  940  992 1023 1274 1404 1425 1435 1498 1500 1522 1595 1604 1610 \n",
       " 337  382  404  412  504  551  559  562  577  578  585  613  618  621 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rs = rstudent(model2b)\n",
    "summary(rs)\n",
    "k = which(abs(rs) > 2)\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = age ~ . - ethnicity, data = gaw2[-k, ])\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-15.3127  -4.7455  -0.1346   3.8465  17.5500 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 16.76080    0.98011  17.101  < 2e-16 ***\n",
       "sexM         2.64491    0.59760   4.426 1.15e-05 ***\n",
       "AgeOnset     0.64691    0.03388  19.093  < 2e-16 ***\n",
       "MaxDinks    -0.04960    0.01647  -3.011  0.00271 ** \n",
       "packsDay     0.26238    0.01232  21.290  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 6.396 on 587 degrees of freedom\n",
       "Multiple R-squared:  0.6913,\tAdjusted R-squared:  0.6892 \n",
       "F-statistic: 328.6 on 4 and 587 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2c = lm(age ~ . - ethnicity, data =gaw2[-k, ])\n",
    "summary(model2c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = age ~ sex + factor(ethnicity) + alcoholDependence + \n",
       "    AgeOnset + MaxDinks + packsDay, data = gaw2)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-42.780  -8.265  -1.316   6.601  45.869 \n",
       "\n",
       "Coefficients:\n",
       "                   Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)        51.82961    8.76901   5.911 4.30e-09 ***\n",
       "sexM                0.39746    0.76050   0.523    0.601    \n",
       "factor(ethnicity)1  3.46936    9.40157   0.369    0.712    \n",
       "factor(ethnicity)3 -1.55100   10.67662  -0.145    0.885    \n",
       "factor(ethnicity)4 -2.44669    8.75887  -0.279    0.780    \n",
       "factor(ethnicity)5 -6.29545    9.31048  -0.676    0.499    \n",
       "factor(ethnicity)6  0.27467    8.71812   0.032    0.975    \n",
       "factor(ethnicity)7 -1.30735    8.82186  -0.148    0.882    \n",
       "factor(ethnicity)8 -2.56055    9.40937  -0.272    0.786    \n",
       "alcoholDependence  -5.48646    0.38193 -14.365  < 2e-16 ***\n",
       "AgeOnset            0.48896    0.04334  11.282  < 2e-16 ***\n",
       "MaxDinks           -0.11025    0.02697  -4.088 4.61e-05 ***\n",
       "packsDay            0.29015    0.01533  18.921  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 12.3 on 1368 degrees of freedom\n",
       "Multiple R-squared:  0.3502,\tAdjusted R-squared:  0.3445 \n",
       "F-statistic: 61.43 on 12 and 1368 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model3 = lm(age ~ sex + factor(ethnicity) + AgeOnset + MaxDinks + packsDay, data =gaw2)\n",
    "summary(model3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "[1] 4380.837"
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       "4379.01216679838"
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      "text/plain": [
       "[1] 4379.012"
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     "data": {
      "text/html": [
       "3884.14279040001"
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       "3884.14279040001"
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       "3884.14279040001"
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      "text/plain": [
       "[1] 3884.143"
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     "data": {
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       "4411.86756072302"
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       "[1] 4411.868"
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       "[1] 4405.61"
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       "[1] 3910.444"
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     "metadata": {},
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   ],
   "source": [
    "AIC(model2) # kryterium Akaike\n",
    "AIC(model2b)\n",
    "AIC(model2c)\n",
    "BIC(model2) # kryterium Schwartza\n",
    "BIC(model2b)\n",
    "BIC(model2c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "-43.305  -8.129  -1.504   0.000   6.405  46.455 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  model5$residuals\n",
       "W = 0.97544, p-value = 1.349e-14\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QD/JvvaNJATQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QE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",
      "text/plain": [
       "Plot with title \"Histogram of model5$residuals\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model2c$residuals)\n",
    "hist(model2c$residuals)\n",
    "shapiro.test(model2c$residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of 13\n",
      " $ coefficients : Named num [1:5] 16.7608 2.6449 0.6469 -0.0496 0.2624\n",
      "  ..- attr(*, \"names\")= chr [1:5] \"(Intercept)\" \"sexM\" \"AgeOnset\" \"MaxDinks\" ...\n",
      " $ residuals    : Named num [1:592] -0.381 -8.771 0.228 6.182 5.444 ...\n",
      "  ..- attr(*, \"names\")= chr [1:592] \"1\" \"2\" \"5\" \"7\" ...\n",
      " $ effects      : Named num [1:592] -899.1 35.01 184.4 2.02 -136.18 ...\n",
      "  ..- attr(*, \"names\")= chr [1:592] \"(Intercept)\" \"sexM\" \"AgeOnset\" \"MaxDinks\" ...\n",
      " $ rank         : int 5\n",
      " $ fitted.values: Named num [1:592] 30.4 39.8 27.8 53.8 32.6 ...\n",
      "  ..- attr(*, \"names\")= chr [1:592] \"1\" \"2\" \"5\" \"7\" ...\n",
      " $ assign       : int [1:5] 0 1 2 3 4\n",
      " $ qr           :List of 5\n",
      "  ..$ qr   : num [1:592, 1:5] -24.3311 0.0411 0.0411 0.0411 0.0411 ...\n",
      "  .. ..- attr(*, \"dimnames\")=List of 2\n",
      "  .. .. ..$ : chr [1:592] \"1\" \"2\" \"5\" \"7\" ...\n",
      "  .. .. ..$ : chr [1:5] \"(Intercept)\" \"sexM\" \"AgeOnset\" \"MaxDinks\" ...\n",
      "  .. ..- attr(*, \"assign\")= int [1:5] 0 1 2 3 4\n",
      "  .. ..- attr(*, \"contrasts\")=List of 1\n",
      "  .. .. ..$ sex: chr \"contr.treatment\"\n",
      "  ..$ qraux: num [1:5] 1.04 1.06 1.03 1 1.02\n",
      "  ..$ pivot: int [1:5] 1 2 3 4 5\n",
      "  ..$ tol  : num 1e-07\n",
      "  ..$ rank : int 5\n",
      "  ..- attr(*, \"class\")= chr \"qr\"\n",
      " $ df.residual  : int 587\n",
      " $ contrasts    :List of 1\n",
      "  ..$ sex: chr \"contr.treatment\"\n",
      " $ xlevels      :List of 1\n",
      "  ..$ sex: chr [1:2] \"F\" \"M\"\n",
      " $ call         : language lm(formula = age ~ . - ethnicity, data = gaw2[-k, ])\n",
      " $ terms        :Classes 'terms', 'formula'  language age ~ (sex + ethnicity + AgeOnset + MaxDinks + packsDay) - ethnicity\n",
      "  .. ..- attr(*, \"variables\")= language list(age, sex, ethnicity, AgeOnset, MaxDinks, packsDay)\n",
      "  .. ..- attr(*, \"factors\")= int [1:6, 1:4] 0 1 0 0 0 0 0 0 0 1 ...\n",
      "  .. .. ..- attr(*, \"dimnames\")=List of 2\n",
      "  .. .. .. ..$ : chr [1:6] \"age\" \"sex\" \"ethnicity\" \"AgeOnset\" ...\n",
      "  .. .. .. ..$ : chr [1:4] \"sex\" \"AgeOnset\" \"MaxDinks\" \"packsDay\"\n",
      "  .. ..- attr(*, \"term.labels\")= chr [1:4] \"sex\" \"AgeOnset\" \"MaxDinks\" \"packsDay\"\n",
      "  .. ..- attr(*, \"order\")= int [1:4] 1 1 1 1\n",
      "  .. ..- attr(*, \"intercept\")= int 1\n",
      "  .. ..- attr(*, \"response\")= int 1\n",
      "  .. ..- attr(*, \".Environment\")=<environment: R_GlobalEnv> \n",
      "  .. ..- attr(*, \"predvars\")= language list(age, sex, ethnicity, AgeOnset, MaxDinks, packsDay)\n",
      "  .. ..- attr(*, \"dataClasses\")= Named chr [1:6] \"numeric\" \"factor\" \"numeric\" \"numeric\" ...\n",
      "  .. .. ..- attr(*, \"names\")= chr [1:6] \"age\" \"sex\" \"ethnicity\" \"AgeOnset\" ...\n",
      " $ model        :'data.frame':\t592 obs. of  6 variables:\n",
      "  ..$ age      : int [1:592] 30 31 28 60 38 40 32 28 22 34 ...\n",
      "  ..$ sex      : Factor w/ 2 levels \"F\",\"M\": 1 1 2 2 1 2 1 1 2 2 ...\n",
      "  ..$ ethnicity: int [1:592] 6 6 6 6 6 6 6 6 6 6 ...\n",
      "  ..$ AgeOnset : int [1:592] 16 30 16 38 18 33 17 15 15 16 ...\n",
      "  ..$ MaxDinks : int [1:592] 24 12 40 24 75 48 36 48 71 26 ...\n",
      "  ..$ packsDay : num [1:592] 17 16 0 42 30 0 32 12 12 0 ...\n",
      "  ..- attr(*, \"terms\")=Classes 'terms', 'formula'  language age ~ (sex + ethnicity + AgeOnset + MaxDinks + packsDay) - ethnicity\n",
      "  .. .. ..- attr(*, \"variables\")= language list(age, sex, ethnicity, AgeOnset, MaxDinks, packsDay)\n",
      "  .. .. ..- attr(*, \"factors\")= int [1:6, 1:4] 0 1 0 0 0 0 0 0 0 1 ...\n",
      "  .. .. .. ..- attr(*, \"dimnames\")=List of 2\n",
      "  .. .. .. .. ..$ : chr [1:6] \"age\" \"sex\" \"ethnicity\" \"AgeOnset\" ...\n",
      "  .. .. .. .. ..$ : chr [1:4] \"sex\" \"AgeOnset\" \"MaxDinks\" \"packsDay\"\n",
      "  .. .. ..- attr(*, \"term.labels\")= chr [1:4] \"sex\" \"AgeOnset\" \"MaxDinks\" \"packsDay\"\n",
      "  .. .. ..- attr(*, \"order\")= int [1:4] 1 1 1 1\n",
      "  .. .. ..- attr(*, \"intercept\")= int 1\n",
      "  .. .. ..- attr(*, \"response\")= int 1\n",
      "  .. .. ..- attr(*, \".Environment\")=<environment: R_GlobalEnv> \n",
      "  .. .. ..- attr(*, \"predvars\")= language list(age, sex, ethnicity, AgeOnset, MaxDinks, packsDay)\n",
      "  .. .. ..- attr(*, \"dataClasses\")= Named chr [1:6] \"numeric\" \"factor\" \"numeric\" \"numeric\" ...\n",
      "  .. .. .. ..- attr(*, \"names\")= chr [1:6] \"age\" \"sex\" \"ethnicity\" \"AgeOnset\" ...\n",
      " - attr(*, \"class\")= chr \"lm\"\n"
     ]
    }
   ],
   "source": [
    "str(model2c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ANOVA\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "             Df Sum Sq Mean Sq F value   Pr(>F)    \n",
       "sex           1   2102  2102.0   14.04 0.000196 ***\n",
       "Residuals   620  92856   149.8                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_aov = aov(age ~ sex, data = gaw2)\n",
    "summary(model_aov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWelch Two Sample t-test\n",
       "\n",
       "data:  gaw2$age[gaw2$sex == \"F\"] and gaw2$age[gaw2$sex == \"M\"]\n",
       "t = -4.0547, df = 475.25, p-value = 5.864e-05\n",
       "alternative hypothesis: true difference in means is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -5.850961 -2.031192\n",
       "sample estimates:\n",
       "mean of x mean of y \n",
       " 35.39698  39.33806 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.test(gaw2$age[gaw2$sex == 'F'], gaw2$age[gaw2$sex == 'M'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                   Df Sum Sq Mean Sq F value Pr(>F)\n",
       "factor(ethnicity)   6    772   128.7    0.84  0.539\n",
       "Residuals         615  94186   153.2               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_aov = aov(age ~ factor(ethnicity), data = gaw2)\n",
    "summary(model_aov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPairwise comparisons using t tests with pooled SD \n",
       "\n",
       "data:  gaw2$age and gaw2$ethnicity \n",
       "\n",
       "  1 3 4 5 6 7\n",
       "3 - - - - - -\n",
       "4 - - - - - -\n",
       "5 - - - - - -\n",
       "6 - - - - - -\n",
       "7 - - - - - -\n",
       "8 - - - - - -\n",
       "\n",
       "P value adjustment method: holm "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pairwise.t.test(gaw2$age, gaw2$ethnicity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  Tukey multiple comparisons of means\n",
       "    95% family-wise confidence level\n",
       "\n",
       "Fit: aov(formula = age ~ factor(ethnicity), data = gaw2)\n",
       "\n",
       "$`factor(ethnicity)`\n",
       "            diff        lwr       upr     p adj\n",
       "3-1   2.80000000 -37.301819 42.901819 0.9999935\n",
       "4-1   8.42337662  -8.471305 25.318058 0.7597742\n",
       "5-1  12.60000000 -10.552796 35.752796 0.6760485\n",
       "6-1   7.92145749  -8.532685 24.375600 0.7887025\n",
       "7-1   7.85882353  -9.675188 25.392835 0.8397239\n",
       "8-1   0.80000000 -21.367114 22.967114 0.9999999\n",
       "4-3   5.62337662 -31.221354 42.468107 0.9993601\n",
       "5-3   9.80000000 -30.301819 49.901819 0.9911861\n",
       "6-3   5.12145749 -31.523361 41.766276 0.9996147\n",
       "7-3   5.05882353 -32.083409 42.201056 0.9996681\n",
       "8-3  -2.00000000 -41.540926 37.540926 0.9999990\n",
       "5-4   4.17662338 -12.718058 21.071305 0.9906258\n",
       "6-4  -0.50191913  -4.987128  3.983290 0.9998944\n",
       "7-4  -0.56455309  -8.102449  6.973342 0.9999901\n",
       "8-4  -7.62337662 -23.139796  7.893043 0.7722323\n",
       "6-5  -4.67854251 -21.132685 11.775600 0.9805051\n",
       "7-5  -4.74117647 -22.275188 12.792835 0.9849645\n",
       "8-5 -11.80000000 -33.967114 10.367114 0.6986642\n",
       "7-6  -0.06263396  -6.553273  6.428005 1.0000000\n",
       "8-6  -7.12145749 -22.157008  7.914094 0.8012773\n",
       "8-7  -7.05882353 -23.269023  9.151376 0.8573731\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TukeyHSD(model_aov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                   Df Sum Sq Mean Sq F value   Pr(>F)    \n",
       "sex                 1   2102  2102.0  14.033 0.000197 ***\n",
       "factor(ethnicity)   6    886   147.7   0.986 0.433467    \n",
       "Residuals         614  91970   149.8                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_aov = aov(age ~ sex + factor(ethnicity), data = gaw2)\n",
    "summary(model_aov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                       Df Sum Sq Mean Sq F value   Pr(>F)    \n",
       "sex                     1   2102  2102.0  13.971 0.000203 ***\n",
       "factor(ethnicity)       6    886   147.7   0.982 0.436457    \n",
       "sex:factor(ethnicity)   5    341    68.2   0.454 0.810793    \n",
       "Residuals             609  91629   150.5                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_aov = aov(age ~ sex + factor(ethnicity)+sex:factor(ethnicity), data = gaw2)\n",
    "summary(model_aov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  Tukey multiple comparisons of means\n",
       "    95% family-wise confidence level\n",
       "\n",
       "Fit: aov(formula = age ~ sex + factor(ethnicity) + sex:factor(ethnicity), data = gaw2)\n",
       "\n",
       "$sex\n",
       "        diff      lwr      upr     p adj\n",
       "M-F 3.941077 1.870375 6.011778 0.0002032\n",
       "\n",
       "$`factor(ethnicity)`\n",
       "            diff        lwr       upr     p adj\n",
       "3-1   1.22356938 -38.525685 40.972823 1.0000000\n",
       "4-1   8.22888194  -8.517266 24.975030 0.7720689\n",
       "5-1  13.38821531  -9.561027 36.337458 0.5989322\n",
       "6-1   7.57362158  -8.735860 23.883103 0.8157465\n",
       "7-1   7.67336110  -9.706496 25.053218 0.8491100\n",
       "8-1  -0.11958453 -22.091811 21.852642 1.0000000\n",
       "4-3   7.00531255 -29.515489 43.526114 0.9976605\n",
       "5-3  12.16464592 -27.584608 51.913900 0.9717053\n",
       "6-3   6.35005220 -29.972594 42.672699 0.9986118\n",
       "7-3   6.44979172 -30.365896 43.265480 0.9985952\n",
       "8-3  -1.34315391 -40.536447 37.850139 0.9999999\n",
       "5-4   5.15933337 -11.586814 21.905481 0.9707438\n",
       "6-4  -0.65526035  -5.101036  3.790516 0.9994763\n",
       "7-4  -0.55552083  -8.027145  6.916103 0.9999905\n",
       "8-4  -8.34846646 -23.728469  7.031536 0.6786972\n",
       "6-5  -5.81459372 -22.124075 10.494888 0.9407663\n",
       "7-5  -5.71485420 -23.094711 11.665003 0.9596972\n",
       "8-5 -13.50779983 -35.480027  8.464427 0.5359012\n",
       "7-6   0.09973952  -6.333836  6.533315 1.0000000\n",
       "8-6  -7.69320611 -22.596569  7.210156 0.7284461\n",
       "8-7  -7.79294563 -23.860629  8.274738 0.7827705\n",
       "\n",
       "$`sex:factor(ethnicity)`\n",
       "               diff         lwr       upr     p adj\n",
       "M:1-F:1  -0.5000000 -38.2055138 37.205514 1.0000000\n",
       "F:3-F:1          NA          NA        NA        NA\n",
       "M:3-F:1   2.5000000 -48.0872552 53.087255 1.0000000\n",
       "F:4-F:1   7.2037037 -23.0652637 37.472671 0.9999408\n",
       "M:4-F:1   8.6200000 -21.1649694 38.404969 0.9994793\n",
       "F:5-F:1  10.5000000 -27.2055138 48.205514 0.9996569\n",
       "M:5-F:1  15.0000000 -26.3043209 56.304321 0.9947147\n",
       "F:6-F:1   4.4155844 -24.9800222 33.811191 0.9999998\n",
       "M:6-F:1   9.0735294 -20.2188117 38.365871 0.9989296\n",
       "F:7-F:1   5.0000000 -26.5466962 36.546696 0.9999995\n",
       "M:7-F:1   8.9545455 -21.5507172 39.459808 0.9993938\n",
       "F:8-F:1   8.5000000 -42.0872552 59.087255 0.9999991\n",
       "M:8-F:1  -1.1000000 -35.6576742 33.457674 1.0000000\n",
       "F:3-M:1          NA          NA        NA        NA\n",
       "M:3-M:1   3.0000000 -44.6941216 50.694122 1.0000000\n",
       "F:4-M:1   7.7037037 -17.4333055 32.840713 0.9990428\n",
       "M:4-M:1   9.1200000 -15.4320518 33.672052 0.9934459\n",
       "F:5-M:1  11.0000000 -22.7248368 44.724837 0.9981760\n",
       "M:5-M:1  15.5000000 -22.2055138 53.205514 0.9834851\n",
       "F:6-M:1   4.9155844 -19.1626326 28.993801 0.9999901\n",
       "M:6-M:1   9.5735294 -14.3785080 33.525567 0.9871253\n",
       "F:7-M:1   5.5000000 -21.1618245 32.161825 0.9999888\n",
       "M:7-M:1   9.4545455 -15.9665068 34.875598 0.9933684\n",
       "F:8-M:1   9.0000000 -38.6941216 56.694122 0.9999961\n",
       "M:8-M:1  -0.6000000 -30.7644111 29.564411 1.0000000\n",
       "M:3-F:3          NA          NA        NA        NA\n",
       "F:4-F:3          NA          NA        NA        NA\n",
       "M:4-F:3          NA          NA        NA        NA\n",
       "F:5-F:3          NA          NA        NA        NA\n",
       "M:5-F:3          NA          NA        NA        NA\n",
       "F:6-F:3          NA          NA        NA        NA\n",
       "M:6-F:3          NA          NA        NA        NA\n",
       "F:7-F:3          NA          NA        NA        NA\n",
       "M:7-F:3          NA          NA        NA        NA\n",
       "F:8-F:3          NA          NA        NA        NA\n",
       "M:8-F:3          NA          NA        NA        NA\n",
       "F:4-M:3   4.7037037 -37.3585579 46.765965 1.0000000\n",
       "M:4-M:3   6.1200000 -35.5953193 47.835319 0.9999998\n",
       "F:5-M:3   8.0000000 -39.6941216 55.694122 0.9999991\n",
       "M:5-M:3  12.5000000 -38.0872552 63.087255 0.9999093\n",
       "F:6-M:3   1.9155844 -39.5226245 43.353793 1.0000000\n",
       "M:6-M:3   6.5735294 -34.7914886 47.938547 0.9999995\n",
       "F:7-M:3   2.5000000 -40.4909003 45.490900 1.0000000\n",
       "M:7-M:3   6.4545455 -35.7780784 48.687169 0.9999997\n",
       "F:8-M:3   6.0000000 -52.4131308 64.413131 1.0000000\n",
       "M:8-M:3  -3.6000000 -48.8466166 41.646617 1.0000000\n",
       "M:4-F:4   1.4162963  -8.4481784 11.280771 0.9999999\n",
       "F:5-F:4   3.2962963 -21.8407129 28.433306 1.0000000\n",
       "M:5-F:4   7.7962963 -22.4726711 38.065264 0.9998552\n",
       "F:6-F:4  -2.7881193 -11.4058423  5.829604 0.9983211\n",
       "M:6-F:4   1.8698257  -6.3887885 10.128440 0.9999667\n",
       "F:7-F:4  -2.2037037 -16.5340038 12.126596 0.9999997\n",
       "M:7-F:4   1.7508418 -10.1123160 13.613999 0.9999998\n",
       "F:8-F:4   1.2962963 -40.7659653 43.358558 1.0000000\n",
       "M:8-F:4  -8.3037037 -28.4133111 11.805904 0.9828265\n",
       "F:5-M:4   1.8800000 -22.6720518 26.432052 1.0000000\n",
       "M:5-M:4   6.3800000 -23.4049694 36.164969 0.9999826\n",
       "F:6-M:4  -4.2044156 -10.9274480  2.518617 0.6971470\n",
       "M:6-M:4   0.4535294  -5.8025655  6.709624 1.0000000\n",
       "F:7-M:4  -3.6200000 -16.8974815  9.657482 0.9997279\n",
       "M:7-M:4   0.3345455 -10.2327875 10.901878 1.0000000\n",
       "F:8-M:4  -0.1200000 -41.8353193 41.595319 1.0000000\n",
       "M:8-M:4  -9.7200000 -29.0934438  9.653444 0.9192230\n",
       "M:5-F:5   4.5000000 -33.2055138 42.205514 1.0000000\n",
       "F:6-F:5  -6.0844156 -30.1626326 17.993801 0.9998832\n",
       "M:6-F:5  -1.4264706 -25.3785080 22.525567 1.0000000\n",
       "F:7-F:5  -5.5000000 -32.1618245 21.161825 0.9999888\n",
       "M:7-F:5  -1.5454545 -26.9665068 23.875598 1.0000000\n",
       "F:8-F:5  -2.0000000 -49.6941216 45.694122 1.0000000\n",
       "M:8-F:5 -11.6000000 -41.7644111 18.564411 0.9909389\n",
       "F:6-M:5 -10.5844156 -39.9800222 18.811191 0.9951319\n",
       "M:6-M:5  -5.9264706 -35.2188117 23.365871 0.9999911\n",
       "F:7-M:5 -10.0000000 -41.5466962 21.546696 0.9986394\n",
       "M:7-M:5  -6.0454545 -36.5507172 24.459808 0.9999930\n",
       "F:8-M:5  -6.5000000 -57.0872552 44.087255 1.0000000\n",
       "M:8-M:5 -16.1000000 -50.6576742 18.457674 0.9534510\n",
       "M:6-F:6   4.6579450   0.6459615  8.669929 0.0077289\n",
       "F:7-F:6   0.5844156 -11.7949545 12.963786 1.0000000\n",
       "M:7-F:6   4.5389610  -4.8751674 13.953089 0.9395524\n",
       "F:8-F:6   4.0844156 -37.3537933 45.522624 1.0000000\n",
       "M:8-F:6  -5.5155844 -24.2849108 13.253742 0.9993867\n",
       "F:7-M:6  -4.0735294 -16.2056505  8.058592 0.9975540\n",
       "M:7-M:6  -0.1189840  -9.2055330  8.967565 1.0000000\n",
       "F:8-M:6  -0.5735294 -41.9385474 40.791489 1.0000000\n",
       "M:8-M:6 -10.1735294 -28.7807100  8.433651 0.8564739\n",
       "M:7-F:7   3.9545455 -10.8683478 18.777439 0.9997858\n",
       "F:8-F:7   3.5000000 -39.4909003 46.490900 1.0000000\n",
       "M:8-F:7  -6.1000000 -28.0859037 15.885904 0.9996704\n",
       "F:8-M:7  -0.4545455 -42.6871693 41.778078 1.0000000\n",
       "M:8-M:7 -10.0545455 -30.5180978 10.409007 0.9305073\n",
       "M:8-F:8  -9.6000000 -54.8466166 35.646617 0.9999844\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TukeyHSD(model_aov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   \n",
       "      1   3   4   5   6   7   8\n",
       "  F   2   0  27   3 154  12   1\n",
       "  M   3   1  50   2 340  22   5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(gaw2$sex, gaw2$ethnicity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                       Df Sum Sq Mean Sq F value   Pr(>F)    \n",
       "sex                     1   2102  2102.0  13.971 0.000203 ***\n",
       "factor(ethnicity)       6    886   147.7   0.982 0.436457    \n",
       "sex:factor(ethnicity)   5    341    68.2   0.454 0.810793    \n",
       "Residuals             609  91629   150.5                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_aov = aov(age ~ sex * factor(ethnicity), data = gaw2)\n",
    "summary(model_aov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>sex</th><td>  1         </td><td> 2102.0004  </td><td>2102.00042  </td><td>13.9707237  </td><td>0.0002031662</td></tr>\n",
       "\t<tr><th scope=row>factor(ethnicity)</th><td>  6         </td><td>  886.4661  </td><td> 147.74435  </td><td> 0.9819672  </td><td>0.4364571083</td></tr>\n",
       "\t<tr><th scope=row>sex:factor(ethnicity)</th><td>  5         </td><td>  341.2008  </td><td>  68.24015  </td><td> 0.4535510  </td><td>0.8107927572</td></tr>\n",
       "\t<tr><th scope=row>Residuals</th><td>609         </td><td>91628.6285  </td><td> 150.45752  </td><td>        NA  </td><td>          NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tsex &   1          &  2102.0004   & 2102.00042   & 13.9707237   & 0.0002031662\\\\\n",
       "\tfactor(ethnicity) &   6          &   886.4661   &  147.74435   &  0.9819672   & 0.4364571083\\\\\n",
       "\tsex:factor(ethnicity) &   5          &   341.2008   &   68.24015   &  0.4535510   & 0.8107927572\\\\\n",
       "\tResiduals & 609          & 91628.6285   &  150.45752   &         NA   &           NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | Sum Sq | Mean Sq | F value | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| sex |   1          |  2102.0004   | 2102.00042   | 13.9707237   | 0.0002031662 |\n",
       "| factor(ethnicity) |   6          |   886.4661   |  147.74435   |  0.9819672   | 0.4364571083 |\n",
       "| sex:factor(ethnicity) |   5          |   341.2008   |   68.24015   |  0.4535510   | 0.8107927572 |\n",
       "| Residuals | 609          | 91628.6285   |  150.45752   |         NA   |           NA |\n",
       "\n"
      ],
      "text/plain": [
       "                      Df  Sum Sq     Mean Sq    F value    Pr(>F)      \n",
       "sex                     1  2102.0004 2102.00042 13.9707237 0.0002031662\n",
       "factor(ethnicity)       6   886.4661  147.74435  0.9819672 0.4364571083\n",
       "sex:factor(ethnicity)   5   341.2008   68.24015  0.4535510 0.8107927572\n",
       "Residuals             609 91628.6285  150.45752         NA           NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_aov = lm(age ~ sex + factor(ethnicity)+sex:factor(ethnicity), data = gaw2)\n",
    "anova(model_aov)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regresja logistyczna"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "  0   1 \n",
       "199 423 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "glm(formula = sex2 ~ age + packsDay, family = binomial(), data = gaw2)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-2.1614  -1.3835   0.7861   0.9294   1.0783  \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error z value Pr(>|z|)  \n",
       "(Intercept) -0.120460   0.308961  -0.390   0.6966  \n",
       "age          0.019888   0.009262   2.147   0.0318 *\n",
       "packsDay     0.007054   0.005015   1.406   0.1596  \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 779.77  on 621  degrees of freedom\n",
       "Residual deviance: 763.27  on 619  degrees of freedom\n",
       "AIC: 769.27\n",
       "\n",
       "Number of Fisher Scoring iterations: 4\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaw2$sex2 = 0\n",
    "gaw2$sex2[gaw2$sex == 'M'] = 1\n",
    "table(gaw2$sex2)\n",
    "\n",
    "model_log = glm(sex2 ~ age + packsDay, data = gaw2, family = binomial())\n",
    "summary(model_log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   \n",
       "p2    0   1\n",
       "  1 199 423"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "  0   1 \n",
       "199 423 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = predict(model_log, type = 'response')\n",
    "p2 = rep(0, length(p))\n",
    "p2[p > 0.5] = 1\n",
    "table(p2, gaw2$sex2)\n",
    "table(gaw2$sex2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   p2\n",
       "      0   1\n",
       "  0 153  46\n",
       "  1 277 146"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "  0   1 \n",
       "199 423 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = predict(model_log, type = 'response')\n",
    "p2 = rep(0, length(p))\n",
    "p2[p > 0.7] = 1\n",
    "table(gaw2$sex2,p2)\n",
    "table(gaw2$sex2)"
   ]
  }
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