Algorithms
Takuma Mimura
6/3/2020
Basics of Logistic Regression
library("ggplot2")
library("tidyverse")## ── Attaching packages ────────────────────────────────────────────────── tidyverse 1.3.0 ──## ✓ tibble 2.1.3 ✓ dplyr 0.8.3
## ✓ tidyr 1.0.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.4.0
## ✓ purrr 0.3.3## ── Conflicts ───────────────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library("dplyr")
library("magrittr")##
## Attaching package: 'magrittr'## The following object is masked from 'package:purrr':
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## set_names## The following object is masked from 'package:tidyr':
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## extract#Basics of Logistic Regression
library(openintro)## Please visit openintro.org for free statistics materials##
## Attaching package: 'openintro'## The following object is masked from 'package:ggplot2':
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## diamonds## The following objects are masked from 'package:datasets':
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## cars, treesdata(email)
head(email)## spam to_multiple from cc sent_email time image attach dollar
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## 6 0 0 1 noneemail <- mutate(email, log_num_char = log(num_char))
email ## spam to_multiple from cc sent_email time image attach
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## 3830 1 0 1 0 0 2012-03-11 07:43:58 0 2
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## 3921 1 0 1 0 0 2012-03-31 18:20:24 0 0
## dollar winner inherit viagra password num_char line_breaks format re_subj
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## 1760 0 no 0 0 8 10.613 225 1 0
## 1761 0 no 0 0 0 9.120 239 0 0
## 1762 0 no 0 0 0 3.791 98 1 0
## 1763 0 no 0 0 0 1.310 32 0 0
## 1764 0 no 0 0 0 49.064 753 1 0
## 1765 0 no 0 0 0 2.128 45 1 1
## 1766 0 no 0 0 0 7.568 208 1 1
## 1767 0 no 0 0 0 5.504 102 1 1
## 1768 0 no 0 0 22 10.113 203 1 0
## 1769 0 no 0 0 22 10.113 203 1 0
## 1770 2 no 0 0 0 18.649 388 1 0
## 1771 44 no 0 0 0 190.087 4022 1 0
## 1772 0 no 0 0 0 1.259 36 1 1
## 1773 4 no 0 0 0 11.648 172 1 0
## 1774 0 no 0 0 0 1.448 32 1 0
## 1775 0 no 0 0 0 38.198 577 1 0
## 1776 0 no 0 0 0 5.127 120 1 1
## 1777 0 no 0 0 0 8.937 211 1 1
## 1778 0 no 0 0 0 0.740 18 1 1
## 1779 0 no 0 0 0 2.286 60 1 1
## 1780 0 no 0 0 11 9.521 201 1 0
## 1781 0 no 0 0 11 9.517 201 1 0
## 1782 0 no 0 0 0 13.337 256 1 1
## 1783 0 no 0 0 0 0.082 6 0 1
## 1784 0 no 0 0 0 0.109 4 0 1
## 1785 0 no 0 0 0 7.347 98 0 0
## 1786 0 no 0 0 0 0.355 23 0 1
## 1787 0 no 0 0 0 0.080 6 0 1
## 1788 63 no 0 0 0 37.104 1332 1 0
## 1789 0 no 0 0 0 7.767 150 1 0
## 1790 0 no 0 0 0 0.244 8 0 1
## 1791 0 no 0 0 0 1.840 46 1 1
## 1792 2 no 0 0 0 14.249 353 1 0
## 1793 0 no 0 0 0 73.318 1425 1 0
## 1794 0 no 0 0 0 15.402 422 1 0
## 1795 0 no 0 0 0 0.667 26 0 1
## 1796 0 no 0 0 0 4.818 58 0 0
## 1797 0 no 0 0 0 0.790 17 0 0
## 1798 2 no 0 0 0 8.526 147 1 0
## 1799 0 no 0 0 0 6.843 199 1 0
## 1800 15 no 0 0 0 16.763 379 1 0
## 1801 20 no 1 0 0 17.677 380 1 0
## 1802 0 no 0 0 0 13.225 255 1 0
## 1803 0 no 0 0 0 25.340 639 1 0
## 1804 27 no 0 0 0 19.133 701 1 0
## 1805 0 no 0 0 0 0.262 8 0 1
## 1806 9 no 0 0 0 1.854 47 0 1
## 1807 0 no 0 0 0 10.419 198 1 0
## 1808 2 no 0 0 0 14.263 209 1 0
## 1809 20 no 0 0 0 46.751 922 1 0
## 1810 15 no 0 0 0 17.700 398 1 0
## 1811 0 no 0 0 0 0.046 3 0 0
## 1812 0 no 0 0 0 0.723 15 0 1
## 1813 0 no 0 0 0 0.907 20 0 1
## 1814 0 no 0 0 0 2.599 86 1 0
## 1815 0 no 0 0 0 24.422 622 1 0
## 1816 0 no 0 0 0 25.173 635 1 0
## 1817 0 no 0 0 0 24.835 630 1 0
## 1818 0 no 0 0 0 25.476 640 1 0
## 1819 0 no 0 0 0 24.947 632 1 0
## 1820 0 no 0 0 0 7.525 178 1 0
## 1821 2 yes 1 0 0 10.218 235 1 0
## 1822 0 no 0 0 0 16.193 306 1 0
## 1823 0 no 0 0 0 8.577 119 1 0
## 1824 4 no 1 0 0 7.875 190 1 0
## 1825 0 no 0 0 0 25.926 649 1 0
## 1826 11 no 0 0 0 19.503 424 1 0
## 1827 16 no 0 0 0 26.765 295 1 0
## 1828 26 no 0 0 0 16.976 216 1 0
## 1829 0 no 0 0 0 4.177 103 1 1
## 1830 0 no 0 0 0 0.649 20 0 0
## 1831 0 no 0 0 0 1.468 40 0 0
## 1832 15 no 0 0 0 22.389 489 1 0
## 1833 0 no 0 0 0 25.022 633 1 0
## 1834 0 no 0 0 0 26.093 651 1 0
## 1835 13 no 0 0 0 16.179 366 1 0
## 1836 0 no 0 0 0 31.362 750 1 0
## 1837 0 no 0 0 0 9.337 179 1 0
## 1838 0 no 0 0 0 25.555 643 1 0
## 1839 0 no 0 0 0 31.462 753 1 0
## 1840 0 no 0 0 0 33.004 778 1 0
## 1841 0 no 0 0 0 6.676 166 1 0
## 1842 0 no 0 0 0 9.404 188 1 0
## 1843 12 no 1 0 0 12.116 270 1 0
## 1844 0 no 0 0 0 0.887 27 0 0
## 1845 0 no 0 0 0 1.027 26 0 0
## 1846 0 no 0 0 0 0.917 28 0 1
## 1847 0 no 0 0 0 2.887 84 1 1
## 1848 0 no 0 0 0 7.449 199 1 1
## 1849 0 no 0 0 0 1.590 35 0 1
## 1850 0 no 0 0 0 1.589 31 1 0
## 1851 0 no 0 0 0 4.187 89 1 1
## 1852 0 no 0 0 0 13.157 320 1 1
## 1853 0 no 0 0 0 3.100 72 0 1
## 1854 0 no 0 0 0 3.503 81 0 1
## 1855 4 no 0 0 0 3.135 68 1 0
## 1856 4 no 0 0 0 4.902 117 1 1
## 1857 0 no 0 0 0 0.651 19 0 0
## 1858 0 no 0 0 0 7.039 182 1 1
## 1859 0 no 0 0 0 9.291 253 1 0
## 1860 0 no 0 0 0 12.151 348 1 1
## 1861 0 no 0 0 0 1.167 33 1 1
## 1862 0 no 0 0 0 14.745 449 1 1
## 1863 0 no 0 0 0 17.162 536 1 1
## 1864 0 no 0 0 0 17.926 560 1 1
## 1865 0 no 0 0 0 6.900 188 1 0
## 1866 0 no 0 0 0 6.491 190 1 1
## 1867 2 no 0 0 0 10.731 357 1 0
## 1868 0 no 0 0 0 3.637 75 1 0
## 1869 0 no 0 0 0 4.946 175 1 0
## 1870 1 no 0 0 0 1.551 45 0 0
## 1871 1 no 0 0 0 1.595 59 0 1
## 1872 0 no 0 0 0 1.176 28 0 0
## 1873 0 no 0 0 0 1.213 34 0 0
## 1874 2 no 0 0 0 7.818 162 1 1
## 1875 0 no 0 0 0 0.900 29 0 1
## 1876 1 no 0 0 0 4.809 88 1 1
## 1877 0 no 0 0 0 5.495 143 1 1
## 1878 0 no 0 0 0 3.568 81 1 0
## 1879 0 no 0 0 0 33.828 437 0 0
## 1880 0 no 0 0 0 9.178 127 0 0
## 1881 0 no 0 0 0 3.153 90 1 1
## 1882 0 no 0 0 0 0.829 31 0 1
## 1883 0 no 0 0 0 1.063 23 1 0
## 1884 0 no 0 0 0 13.224 174 0 0
## 1885 0 no 0 0 0 1.380 51 0 1
## 1886 0 no 0 0 0 1.195 25 1 0
## 1887 0 no 0 0 0 2.734 84 1 0
## 1888 0 no 0 0 0 0.601 16 1 0
## 1889 1 no 0 0 0 11.289 153 0 0
## 1890 2 no 0 0 0 8.678 149 1 0
## 1891 0 no 0 0 0 25.739 646 1 0
## 1892 0 no 0 0 0 17.318 311 1 0
## 1893 0 no 0 0 0 26.316 656 1 0
## 1894 0 no 0 0 0 0.266 11 0 0
## 1895 0 no 0 0 0 34.408 807 1 0
## 1896 0 no 0 0 0 0.076 6 0 1
## 1897 0 no 0 0 0 4.560 70 0 0
## 1898 6 no 0 0 0 7.501 145 1 0
## 1899 0 no 0 0 0 9.491 233 1 1
## 1900 0 no 0 0 0 0.331 16 0 1
## 1901 0 no 0 0 0 3.096 42 1 1
## 1902 0 no 0 0 0 1.643 48 1 1
## 1903 0 no 0 0 0 3.451 91 1 1
## 1904 0 no 0 0 0 1.447 55 0 0
## 1905 0 no 0 0 0 2.977 81 1 1
## 1906 0 no 0 0 0 4.316 127 1 1
## 1907 0 no 0 0 0 1.446 40 1 0
## 1908 0 no 0 0 0 10.761 299 1 0
## 1909 0 no 0 0 0 25.189 636 1 0
## 1910 0 no 0 0 0 3.967 100 1 0
## 1911 0 no 0 0 0 26.877 667 1 0
## 1912 0 no 0 0 0 0.349 13 0 0
## 1913 6 no 0 0 0 19.838 195 1 0
## 1914 0 no 0 0 0 24.957 632 1 0
## 1915 0 no 0 0 0 24.542 624 1 0
## 1916 0 no 0 0 0 25.200 636 1 0
## 1917 0 no 0 0 0 10.486 234 1 0
## 1918 0 no 0 0 0 1.028 22 1 0
## 1919 0 no 0 0 0 26.630 663 1 0
## 1920 0 no 0 0 2 25.209 725 1 0
## 1921 0 no 0 0 0 24.656 822 1 0
## 1922 16 no 1 0 0 14.096 312 1 0
## 1923 0 no 0 0 0 10.091 136 0 0
## 1924 0 no 0 0 0 4.312 124 1 1
## 1925 0 no 0 0 0 9.861 179 1 0
## 1926 5 no 0 0 0 20.966 498 1 0
## 1927 0 no 0 0 0 32.008 499 1 0
## 1928 0 no 0 0 0 15.472 302 1 0
## 1929 0 no 0 0 0 14.043 255 1 0
## 1930 0 no 0 0 0 2.529 79 1 0
## 1931 0 no 0 0 0 4.197 98 1 1
## 1932 0 no 0 0 0 2.014 50 1 1
## 1933 0 no 0 0 0 6.071 157 1 1
## 1934 0 no 0 0 0 1.307 35 0 0
## 1935 0 no 0 0 0 10.081 214 1 1
## 1936 0 no 0 0 0 8.006 214 1 1
## 1937 0 no 0 0 0 2.784 71 1 1
## 1938 0 no 0 0 0 0.732 20 1 0
## 1939 4 no 0 0 0 7.278 201 1 1
## 1940 0 no 0 0 0 13.622 311 1 1
## 1941 1 no 0 0 0 23.601 408 1 0
## 1942 0 no 0 0 0 24.540 624 1 0
## 1943 0 no 0 0 0 3.778 98 1 0
## 1944 4 no 0 0 0 9.049 254 1 1
## 1945 0 no 0 0 0 5.569 95 1 0
## 1946 0 no 0 0 0 0.232 12 0 0
## 1947 0 no 0 0 0 0.340 12 0 0
## 1948 0 no 0 0 0 12.290 139 1 0
## 1949 0 no 0 0 0 0.006 3 0 0
## 1950 0 no 0 0 0 19.343 446 1 0
## 1951 0 no 0 0 0 4.350 62 1 0
## 1952 0 no 0 0 0 1.485 36 1 0
## 1953 0 no 0 0 0 24.846 539 1 0
## 1954 0 no 0 0 0 19.986 452 1 0
## 1955 0 no 0 0 0 0.054 3 0 0
## 1956 0 no 0 0 0 19.997 452 1 0
## 1957 0 no 0 0 0 1.881 26 1 1
## 1958 0 no 0 0 0 24.709 541 1 0
## 1959 0 no 0 0 0 1.212 29 0 1
## 1960 4 no 0 0 0 22.227 356 1 0
## 1961 2 yes 0 0 0 2.152 41 0 1
## 1962 0 no 0 0 0 0.299 4 1 0
## 1963 1 no 0 0 0 7.714 138 1 1
## 1964 12 no 0 0 0 17.778 188 1 0
## 1965 0 no 0 0 0 5.242 56 0 0
## 1966 4 no 0 0 0 10.286 296 1 1
## 1967 0 no 0 0 0 19.985 424 1 0
## 1968 0 no 0 0 0 7.015 170 1 1
## 1969 0 no 0 0 0 0.545 13 1 1
## 1970 0 no 0 0 0 1.732 45 1 1
## 1971 0 no 0 0 0 7.505 168 1 0
## 1972 0 no 0 0 0 24.433 621 1 0
## 1973 20 no 1 0 0 20.623 407 1 0
## 1974 0 no 0 0 0 11.933 165 0 0
## 1975 4 yes 1 0 0 8.575 199 1 0
## 1976 0 no 0 0 2 2.100 53 1 1
## 1977 4 no 0 0 0 11.743 347 1 1
## 1978 0 no 0 0 0 25.653 645 1 0
## 1979 4 yes 0 0 0 7.661 92 1 0
## 1980 2 no 0 0 0 8.118 136 1 0
## 1981 2 no 0 0 0 11.630 175 1 1
## 1982 0 no 0 0 0 0.705 21 1 0
## 1983 0 no 0 0 0 3.859 82 1 1
## 1984 6 no 0 0 0 46.305 1345 1 0
## 1985 0 no 0 0 0 1.407 32 0 1
## 1986 0 no 0 0 0 5.324 129 1 1
## 1987 0 no 0 0 0 2.043 50 1 0
## 1988 0 no 0 0 0 33.360 439 0 0
## 1989 0 no 0 0 0 7.111 150 1 1
## 1990 0 no 0 0 0 0.812 24 0 0
## 1991 2 no 0 0 0 12.388 228 1 1
## 1992 1 no 0 0 0 9.089 152 1 0
## 1993 0 no 0 0 0 13.176 184 0 1
## 1994 0 no 0 0 0 12.974 168 0 0
## 1995 0 no 0 0 0 0.999 36 0 0
## 1996 1 no 0 0 0 26.636 661 1 0
## 1997 0 no 0 0 0 2.575 53 1 0
## 1998 1 no 0 0 0 27.995 687 1 0
## 1999 0 no 0 0 0 0.775 24 0 0
## 2000 0 no 0 0 0 2.969 80 1 0
## 2001 1 no 0 0 0 29.379 711 1 0
## 2002 0 no 0 0 0 17.339 311 1 0
## 2003 10 no 0 0 0 13.975 166 1 0
## 2004 1 no 0 0 0 30.652 735 1 0
## 2005 0 no 0 0 0 7.922 229 1 1
## 2006 0 no 0 0 0 3.184 77 1 1
## 2007 0 no 0 0 0 3.021 73 1 1
## 2008 0 no 0 0 0 2.538 61 1 1
## 2009 0 no 0 0 0 23.050 537 1 1
## 2010 0 no 0 0 0 5.905 94 1 0
## 2011 0 no 0 0 0 24.707 626 1 0
## 2012 0 no 0 0 0 25.542 642 1 0
## 2013 0 no 0 0 0 26.255 654 1 0
## 2014 0 no 0 0 0 26.807 664 1 0
## 2015 0 no 0 0 0 27.266 673 1 0
## 2016 9 no 0 0 0 39.245 667 1 0
## 2017 0 no 0 0 0 26.158 652 1 0
## 2018 0 no 0 0 0 46.703 752 1 0
## 2019 0 no 0 0 0 8.664 211 1 0
## 2020 0 no 0 0 0 3.720 84 1 0
## 2021 8 no 1 0 0 11.427 249 1 0
## 2022 0 no 0 0 0 9.786 196 1 0
## 2023 0 no 0 0 0 25.415 639 1 0
## 2024 0 no 0 0 0 2.342 63 1 0
## 2025 0 no 0 0 0 5.731 96 0 0
## 2026 0 no 0 0 0 5.528 61 0 0
## 2027 21 no 0 0 0 16.182 553 1 0
## 2028 0 no 0 0 0 3.529 80 1 0
## 2029 0 no 0 0 0 6.988 156 1 0
## 2030 0 no 0 0 0 24.439 621 1 0
## 2031 0 no 0 0 0 4.266 78 1 0
## 2032 0 no 0 0 0 0.458 14 1 1
## 2033 0 no 0 0 4 0.413 19 0 0
## 2034 0 no 0 0 0 25.959 648 1 0
## 2035 0 no 0 0 0 25.572 643 1 0
## 2036 0 no 0 0 0 25.093 635 1 0
## 2037 0 no 0 0 0 3.199 26 1 0
## 2038 0 no 0 0 0 18.539 524 1 1
## 2039 0 no 0 0 0 0.517 20 1 0
## 2040 0 no 0 0 0 25.101 635 1 0
## 2041 0 no 0 0 0 1.132 24 1 0
## 2042 1 no 0 0 0 0.517 17 0 0
## 2043 0 no 0 0 0 1.791 41 1 1
## 2044 0 no 0 0 0 2.266 68 1 1
## 2045 0 no 0 0 0 0.574 17 0 1
## 2046 0 no 0 0 0 0.715 13 0 0
## 2047 0 no 0 0 0 11.002 209 1 0
## 2048 0 no 0 0 0 26.904 665 1 0
## 2049 2 no 0 0 0 9.585 150 1 0
## 2050 0 no 0 0 0 2.117 36 1 1
## 2051 0 no 0 0 0 0.239 4 1 0
## 2052 0 no 0 0 0 7.011 183 1 0
## 2053 0 no 0 0 0 2.077 19 0 0
## 2054 0 no 0 0 0 28.464 693 1 0
## 2055 0 no 0 0 0 1.763 45 1 1
## 2056 0 no 0 0 0 6.457 134 1 0
## 2057 0 no 0 0 0 0.353 19 0 0
## 2058 0 no 0 0 0 25.579 642 1 0
## 2059 0 no 0 0 0 3.233 48 0 0
## 2060 11 no 0 0 0 16.341 357 1 0
## 2061 0 no 0 0 0 4.777 187 1 0
## 2062 0 no 0 0 0 25.385 638 1 0
## 2063 2 yes 0 0 0 10.907 153 1 0
## 2064 0 no 0 0 0 22.428 498 1 0
## 2065 0 no 0 0 0 27.182 671 1 0
## 2066 0 no 0 0 0 72.806 1045 1 0
## 2067 1 no 0 0 0 2.531 39 0 1
## 2068 16 no 1 0 0 20.340 404 1 0
## 2069 0 no 0 0 0 9.610 196 1 0
## 2070 0 no 0 0 0 34.473 446 0 0
## 2071 1 no 0 0 0 38.726 513 1 0
## 2072 4 no 0 0 0 9.989 299 1 0
## 2073 0 no 0 0 0 5.950 168 1 0
## 2074 0 no 0 0 0 1.019 31 0 1
## 2075 0 no 0 0 0 0.654 18 1 0
## 2076 0 no 0 0 0 0.266 4 1 0
## 2077 0 no 0 0 2 10.810 295 1 0
## 2078 0 no 0 0 0 7.116 121 1 0
## 2079 0 no 0 0 0 0.781 22 1 0
## 2080 0 no 0 0 0 7.183 254 1 1
## 2081 0 no 0 0 2 11.355 314 1 0
## 2082 0 yes 0 0 0 18.315 417 1 0
## 2083 0 no 0 0 0 2.026 62 1 1
## 2084 0 no 0 0 0 5.967 247 1 1
## 2085 0 no 0 0 0 1.102 27 1 0
## 2086 0 no 0 0 0 24.482 623 1 0
## 2087 4 no 0 0 0 10.144 148 1 0
## 2088 0 no 0 0 0 10.159 258 1 1
## 2089 0 no 0 0 0 24.761 627 1 0
## 2090 0 no 0 0 0 25.907 650 1 0
## 2091 0 no 0 0 0 25.690 644 1 0
## 2092 0 no 0 0 0 3.592 91 1 1
## 2093 0 no 0 0 0 95.308 2355 1 0
## 2094 0 no 0 0 0 7.538 137 1 0
## 2095 0 no 0 0 0 25.354 638 1 0
## 2096 0 no 0 0 0 1.034 41 0 0
## 2097 0 no 0 0 0 6.912 155 1 0
## 2098 0 no 0 0 0 9.548 394 1 1
## 2099 0 no 0 0 0 24.644 626 1 0
## 2100 0 no 0 0 0 25.731 642 1 0
## 2101 16 no 0 0 0 66.956 1235 1 0
## 2102 0 no 0 0 0 0.004 2 0 0
## 2103 0 no 0 0 0 1.138 58 0 1
## 2104 0 no 0 0 0 1.033 26 0 0
## 2105 0 no 0 0 0 3.708 75 1 0
## 2106 0 no 0 0 0 9.383 176 1 0
## 2107 0 no 0 0 0 2.432 55 1 0
## 2108 2 no 0 0 0 0.592 17 0 0
## 2109 6 no 1 0 0 8.651 198 1 0
## 2110 0 no 0 0 3 1.422 36 1 0
## 2111 0 no 0 0 0 9.929 200 1 0
## 2112 0 no 0 0 0 27.884 682 1 0
## 2113 0 no 0 0 0 7.521 126 1 0
## 2114 2 no 0 0 0 28.441 907 1 0
## 2115 0 no 0 0 0 26.586 662 1 0
## 2116 0 no 0 0 0 6.428 206 1 0
## 2117 0 no 0 0 0 27.723 682 1 0
## 2118 0 no 0 0 0 29.643 715 1 0
## 2119 0 no 0 0 0 31.042 740 1 0
## 2120 0 no 0 0 0 10.786 231 1 1
## 2121 0 no 0 0 5 1.999 42 0 0
## 2122 14 no 1 0 0 17.796 356 1 0
## 2123 0 no 0 0 0 9.603 196 1 0
## 2124 0 no 0 0 0 25.460 513 1 0
## 2125 8 no 0 0 0 8.691 304 1 0
## 2126 0 no 0 0 0 10.747 264 1 1
## 2127 0 no 0 0 0 12.862 326 1 1
## 2128 0 no 0 0 0 5.778 146 1 0
## 2129 4 no 0 0 0 8.120 208 1 1
## 2130 2 no 0 0 0 2.317 53 1 1
## 2131 0 no 0 0 0 10.383 137 0 0
## 2132 0 no 0 0 0 12.531 300 1 1
## 2133 6 no 0 0 0 9.246 146 1 0
## 2134 0 no 0 0 0 0.720 17 0 0
## 2135 0 no 0 0 0 0.623 25 0 0
## 2136 0 no 0 0 0 24.518 625 1 0
## 2137 0 no 0 0 0 24.751 630 1 0
## 2138 0 no 0 0 0 3.856 81 1 0
## 2139 0 no 0 0 0 17.429 320 1 0
## 2140 10 no 1 0 0 17.383 353 1 0
## 2141 0 no 0 0 0 25.131 634 1 0
## 2142 0 no 0 0 0 2.855 63 1 1
## 2143 0 no 0 0 0 1.300 26 1 0
## 2144 0 no 0 0 0 13.629 341 1 1
## 2145 0 no 0 0 0 7.284 135 1 0
## 2146 0 no 0 0 0 24.681 626 1 0
## 2147 0 no 0 0 0 2.883 93 0 1
## 2148 0 no 0 0 0 15.588 390 1 1
## 2149 0 no 0 0 0 26.175 656 1 0
## 2150 2 no 0 0 0 24.904 632 1 0
## 2151 2 no 0 0 0 26.687 663 1 0
## 2152 0 no 0 0 0 14.526 316 1 1
## 2153 0 no 0 0 0 6.282 227 0 1
## 2154 0 no 0 0 0 5.242 56 0 0
## 2155 0 no 0 0 0 4.001 132 0 1
## 2156 0 no 0 0 0 2.375 50 0 1
## 2157 46 yes 0 0 0 25.588 282 1 0
## 2158 0 no 0 0 0 29.098 704 1 0
## 2159 0 no 0 0 0 0.667 9 1 0
## 2160 0 no 0 0 0 16.573 309 1 0
## 2161 0 no 0 0 0 0.397 14 0 1
## 2162 0 no 0 0 0 10.103 279 1 1
## 2163 0 no 0 0 0 24.503 623 1 0
## 2164 0 no 0 0 0 25.894 650 1 0
## 2165 0 no 0 0 0 24.889 629 1 0
## 2166 0 no 0 0 0 0.693 25 1 0
## 2167 0 no 0 0 0 1.643 18 1 0
## 2168 0 no 0 0 0 3.889 84 1 0
## 2169 16 no 1 0 0 17.603 356 1 0
## 2170 0 no 0 0 0 7.485 89 0 0
## 2171 4 no 0 0 0 7.721 164 1 0
## 2172 0 no 0 0 0 16.593 435 1 0
## 2173 0 no 0 0 0 2.500 61 1 1
## 2174 0 no 0 0 0 2.061 73 1 0
## 2175 0 no 0 0 0 6.190 129 1 0
## 2176 0 no 0 0 0 5.246 56 0 0
## 2177 0 no 0 0 0 2.928 79 1 1
## 2178 0 no 0 0 0 3.618 49 0 0
## 2179 0 no 0 0 0 2.984 28 1 0
## 2180 0 no 0 0 0 11.910 312 1 0
## 2181 0 no 0 0 0 24.580 626 1 0
## 2182 0 no 0 0 0 1.888 35 0 0
## 2183 0 no 0 0 0 11.240 159 0 0
## 2184 0 no 0 0 0 3.746 98 1 0
## 2185 0 no 0 0 0 16.510 428 1 1
## 2186 0 no 0 0 0 4.047 98 1 1
## 2187 0 no 0 0 0 0.741 27 0 0
## 2188 0 no 0 0 0 5.389 136 1 1
## 2189 0 no 0 0 0 16.925 382 1 0
## 2190 0 no 0 0 0 11.780 348 1 1
## 2191 0 no 0 0 0 5.506 170 1 1
## 2192 0 no 0 0 0 0.361 15 0 0
## 2193 0 no 0 0 0 1.225 45 0 1
## 2194 0 no 0 0 0 5.462 122 1 0
## 2195 0 no 0 0 0 7.912 179 1 1
## 2196 0 no 0 0 0 11.569 260 1 1
## 2197 0 no 0 0 0 5.895 148 1 0
## 2198 0 no 0 0 0 8.267 195 1 1
## 2199 0 no 0 0 0 11.151 276 1 1
## 2200 0 no 0 0 0 2.148 54 0 1
## 2201 0 no 0 0 0 10.914 294 1 1
## 2202 0 no 0 0 0 15.586 376 1 1
## 2203 0 no 0 0 0 14.420 417 1 1
## 2204 0 no 0 0 0 18.172 551 1 1
## 2205 0 no 0 0 0 13.704 340 1 1
## 2206 0 no 0 0 0 5.227 124 0 1
## 2207 0 no 0 0 0 19.395 482 1 1
## 2208 0 no 0 0 0 23.519 515 1 1
## 2209 0 no 0 0 0 23.466 552 1 1
## 2210 0 no 0 0 4 4.033 59 1 1
## 2211 0 no 0 0 0 25.254 812 1 0
## 2212 0 no 0 0 0 29.007 926 1 1
## 2213 0 no 0 0 0 8.879 203 0 1
## 2214 0 no 0 0 0 1.583 38 1 0
## 2215 0 no 0 0 0 19.437 253 1 0
## 2216 0 no 0 0 4 6.890 129 1 1
## 2217 0 no 0 0 0 0.963 20 0 0
## 2218 0 no 0 0 0 26.217 633 1 1
## 2219 0 no 0 0 0 0.661 12 0 0
## 2220 0 no 0 0 2 1.982 49 0 0
## 2221 0 no 0 0 0 1.275 23 0 0
## 2222 0 no 0 0 0 31.113 720 1 1
## 2223 0 no 0 0 0 4.742 167 1 0
## 2224 0 no 0 0 0 0.781 28 1 1
## 2225 0 no 0 0 0 5.727 139 1 1
## 2226 0 no 0 0 0 12.987 168 0 0
## 2227 0 no 0 0 0 30.279 983 1 1
## 2228 6 no 0 0 0 9.692 152 1 0
## 2229 0 no 0 0 0 0.417 20 0 0
## 2230 0 no 0 0 0 64.202 1139 1 0
## 2231 0 no 0 0 0 1.690 47 0 0
## 2232 0 no 0 0 0 4.659 104 1 0
## 2233 0 no 0 0 0 23.352 782 1 0
## 2234 20 no 1 0 0 23.612 455 1 0
## 2235 0 no 0 0 0 8.645 184 1 0
## 2236 0 no 0 0 0 1.027 21 0 1
## 2237 2 no 0 0 0 31.398 652 1 0
## 2238 0 no 0 0 0 5.574 61 0 0
## 2239 0 no 0 0 0 1.122 32 1 1
## 2240 0 no 0 0 0 7.777 237 1 1
## 2241 4 no 0 0 0 9.027 148 1 0
## 2242 0 no 0 0 0 0.083 6 0 0
## 2243 0 no 0 0 0 16.280 396 1 0
## 2244 0 no 0 0 0 0.822 40 0 0
## 2245 0 no 0 0 0 33.343 436 0 0
## 2246 0 no 0 0 2 24.474 601 1 1
## 2247 2 no 0 0 0 28.468 575 1 0
## 2248 0 no 0 0 0 0.286 11 0 0
## 2249 0 no 0 0 0 0.325 10 1 0
## 2250 0 no 0 0 0 9.129 232 1 1
## 2251 0 no 0 0 0 1.926 56 1 1
## 2252 4 no 0 0 0 64.401 1167 1 0
## 2253 0 no 0 0 0 2.110 44 0 1
## 2254 0 no 0 0 0 7.441 147 1 0
## 2255 0 no 0 0 0 11.778 323 1 1
## 2256 0 no 0 0 0 1.698 41 1 0
## 2257 0 no 0 0 0 0.008 3 0 0
## 2258 0 no 0 0 0 0.272 13 0 1
## 2259 0 no 0 0 0 1.524 48 1 1
## 2260 0 no 0 0 0 31.707 609 1 0
## 2261 0 no 0 0 0 22.189 699 1 1
## 2262 2 no 0 0 0 28.651 605 1 0
## 2263 0 no 0 0 0 1.692 41 1 1
## 2264 0 no 0 0 0 1.096 26 0 0
## 2265 0 no 0 0 5 1.222 35 0 0
## 2266 0 no 0 0 0 11.545 325 1 1
## 2267 0 no 0 0 0 3.890 100 1 0
## 2268 0 no 0 0 0 0.298 12 0 0
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## 3921 1 0 1 small 0.7997569156#linear
qplot(x = log_num_char, y = spam, data = email,
geom = "point", alpha = I(.1), ylab = "spam") +
stat_smooth(method = "lm",
se = FALSE)## `geom_smooth()` using formula 'y ~ x'
# logistic
library(dplyr)
email <- mutate(email, log_num_char = log(num_char))
qplot(x = log_num_char, y = spam, data = email,
geom = "point", alpha = I(.1), ylab = "spam") +
stat_smooth(method = "glm", method.args = list(family = "binomial"),
se = FALSE)## `geom_smooth()` using formula 'y ~ x'
m1 <- glm(spam ~ log(num_char), data = email, family = "binomial")
summary(m1)##
## Call:
## glm(formula = spam ~ log(num_char), family = "binomial", data = email)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8149 -0.4674 -0.3347 -0.2545 3.0129
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.72435 0.06062 -28.45 <2e-16 ***
## log(num_char) -0.54350 0.03646 -14.91 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2437.2 on 3920 degrees of freedom
## Residual deviance: 2190.3 on 3919 degrees of freedom
## AIC: 2194.3
##
## Number of Fisher Scoring iterations: 5#Interpreting Log. Reg.
#1, Each row of the summary output is still a H-test on that parameter being 0.
#2, A positive slope estimate indicates that there is a positive association.
#3, Each estimate is still conditional on the other variables held constant.
m2 <- glm(spam ~ log(num_char) + to_multiple + attach + dollar + inherit +
viagra, data = email, family = "binomial")
summary(m2)##
## Call:
## glm(formula = spam ~ log(num_char) + to_multiple + attach + dollar +
## inherit + viagra, family = "binomial", data = email)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9315 -0.4549 -0.3275 -0.2358 3.0335
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.596420 0.064433 -24.777 < 2e-16 ***
## log(num_char) -0.548689 0.038314 -14.321 < 2e-16 ***
## to_multiple -1.928889 0.304931 -6.326 2.52e-10 ***
## attach 0.199698 0.065522 3.048 0.00231 **
## dollar -0.004557 0.018978 -0.240 0.81021
## inherit 0.400030 0.151663 2.638 0.00835 **
## viagra 1.736070 40.592963 0.043 0.96589
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2437.2 on 3920 degrees of freedom
## Residual deviance: 2106.3 on 3914 degrees of freedom
## AIC: 2120.3
##
## Number of Fisher Scoring iterations: 11#Comparing Models
#Confusion matrix
pred1 <- predict(m1, newdata = email, type = "response")
conf_mat1<-data.frame(spam=email$spam, predSpam=pred1>.5)%>%
group_by(spam, predSpam)%>%
summarise(n=n())
conf_mat1## # A tibble: 4 x 3
## # Groups: spam [2]
## spam predSpam n
## <dbl> <lgl> <int>
## 1 0 FALSE 3541
## 2 0 TRUE 13
## 3 1 FALSE 362
## 4 1 TRUE 5pred2<-predict(m2, newdata = email, type = "response")
conf_mat2<-data.frame(spam=email$spam, predSpam=pred2>.5)%>%
group_by(spam, predSpam)%>%
summarise(n=n())
conf_mat2## # A tibble: 4 x 3
## # Groups: spam [2]
## spam predSpam n
## <dbl> <lgl> <int>
## 1 0 FALSE 3537
## 2 0 TRUE 17
## 3 1 FALSE 357
## 4 1 TRUE 10#Test-train
#In the test-train paradigm, you balance descriptive power with predictive accuracy by separating your data set into:
#Training set: used to fit your model
#Testing set: used to evaluate predictive accuracy
#Related to cross-validation…
#Dividing the data
set.seed(501)
train_indices <- sample(1:nrow(email), size = floor(nrow(email)/2))
train_data <- email %>%
slice(train_indices)
test_data <- email %>%
slice(-train_indices)
#Training
m1 <- glm(spam ~ log(num_char), data = train_data, family = "binomial")
m2 <- glm(spam ~ log(num_char) + to_multiple + attach + dollar + inherit +
viagra, data = train_data, family = "binomial")
#Testing
test1 <- predict(m1, newdata = test_data, type = "response")
test_mat1<-data.frame(spam=test_data$spam, predSpam=test1>.5)%>%
group_by(spam, predSpam)%>%
summarise(n=n())
test_mat1## # A tibble: 4 x 3
## # Groups: spam [2]
## spam predSpam n
## <dbl> <lgl> <int>
## 1 0 FALSE 1783
## 2 0 TRUE 4
## 3 1 FALSE 171
## 4 1 TRUE 3test2<-predict(m2, newdata = test_data, type = "response")
test_mat2<-data.frame(spam=test_data$spam, predSpam=test2>.5)%>%
group_by(spam, predSpam)%>%
summarise(n=n())
test_mat2## # A tibble: 4 x 3
## # Groups: spam [2]
## spam predSpam n
## <dbl> <lgl> <int>
## 1 0 FALSE 1782
## 2 0 TRUE 5
## 3 1 FALSE 171
## 4 1 TRUE 3#Extending the model
#A GLM consists of three things:
# A linear predictor
#A distribution of the response
#A link function between the two
#MLR
#Normal distribution, identity link function
#Logisitic Regression
#Binomial distribution, logit link function
#Poisson Regression
#### Advanced Logistic Regression Models
install.packages("titanic", repos = "http://cran.us.r-project.org")##
## The downloaded binary packages are in
## /var/folders/1m/pcxtsxrd3ld0k9h22g50195r0000gn/T//RtmpP0zjiX/downloaded_packageslibrary(tidyverse)
library(titanic)
# LINEAR MODEL
lm_t=lm(Survived ~ Fare, data=titanic_train)
ggplot(titanic_train, aes(x=Fare, y=Survived)) + geom_point() +
stat_smooth(method="lm", se=TRUE)## `geom_smooth()` using formula 'y ~ x'