library('MASS')
dat = Melanoma
dat## time status sex age year thickness ulcer
## 1 10 3 1 76 1972 6.76 1
## 2 30 3 1 56 1968 0.65 0
## 3 35 2 1 41 1977 1.34 0
## 4 99 3 0 71 1968 2.90 0
## 5 185 1 1 52 1965 12.08 1
## 6 204 1 1 28 1971 4.84 1
## 7 210 1 1 77 1972 5.16 1
## 8 232 3 0 60 1974 3.22 1
## 9 232 1 1 49 1968 12.88 1
## 10 279 1 0 68 1971 7.41 1
## 11 295 1 0 53 1969 4.19 1
## 12 355 3 0 64 1972 0.16 1
## 13 386 1 0 68 1965 3.87 1
## 14 426 1 1 63 1970 4.84 1
## 15 469 1 0 14 1969 2.42 1
## 16 493 3 1 72 1971 12.56 1
## 17 529 1 1 46 1971 5.80 1
## 18 621 1 1 72 1972 7.06 1
## 19 629 1 1 95 1968 5.48 1
## 20 659 1 1 54 1972 7.73 1
## 21 667 1 0 89 1968 13.85 1
## 22 718 1 1 25 1967 2.34 1
## 23 752 1 1 37 1973 4.19 1
## 24 779 1 1 43 1967 4.04 1
## 25 793 1 1 68 1970 4.84 1
## 26 817 1 0 67 1966 0.32 0
## 27 826 3 0 86 1965 8.54 1
## 28 833 1 0 56 1971 2.58 1
## 29 858 1 0 16 1967 3.56 0
## 30 869 1 0 42 1965 3.54 0
## 31 872 1 0 65 1968 0.97 0
## 32 967 1 1 52 1970 4.83 1
## 33 977 1 1 58 1967 1.62 1
## 34 982 1 0 60 1970 6.44 1
## 35 1041 1 1 68 1967 14.66 0
## 36 1055 1 0 75 1967 2.58 1
## 37 1062 1 1 19 1966 3.87 1
## 38 1075 1 1 66 1971 3.54 1
## 39 1156 1 0 56 1970 1.34 1
## 40 1228 1 1 46 1973 2.24 1
## 41 1252 1 0 58 1971 3.87 1
## 42 1271 1 0 74 1971 3.54 1
## 43 1312 1 0 65 1970 17.42 1
## 44 1427 3 1 64 1972 1.29 0
## 45 1435 1 1 27 1969 3.22 0
## 46 1499 2 1 73 1973 1.29 0
## 47 1506 1 1 56 1970 4.51 1
## 48 1508 2 1 63 1973 8.38 1
## 49 1510 2 0 69 1973 1.94 0
## 50 1512 2 0 77 1973 0.16 0
## 51 1516 1 1 80 1968 2.58 1
## 52 1525 3 0 76 1970 1.29 1
## 53 1542 2 0 65 1973 0.16 0
## 54 1548 1 0 61 1972 1.62 0
## 55 1557 2 0 26 1973 1.29 0
## 56 1560 1 0 57 1973 2.10 0
## 57 1563 2 0 45 1973 0.32 0
## 58 1584 1 1 31 1970 0.81 0
## 59 1605 2 0 36 1973 1.13 0
## 60 1621 1 0 46 1972 5.16 1
## 61 1627 2 0 43 1973 1.62 0
## 62 1634 2 0 68 1973 1.37 0
## 63 1641 2 1 57 1973 0.24 0
## 64 1641 2 0 57 1973 0.81 0
## 65 1648 2 0 55 1973 1.29 0
## 66 1652 2 0 58 1973 1.29 0
## 67 1654 2 1 20 1973 0.97 0
## 68 1654 2 0 67 1973 1.13 0
## 69 1667 1 0 44 1971 5.80 1
## 70 1678 2 0 59 1973 1.29 0
## 71 1685 2 0 32 1973 0.48 0
## 72 1690 1 1 83 1971 1.62 0
## 73 1710 2 0 55 1973 2.26 0
## 74 1710 2 1 15 1973 0.58 0
## 75 1726 1 0 58 1970 0.97 1
## 76 1745 2 0 47 1973 2.58 1
## 77 1762 2 0 54 1973 0.81 0
## 78 1779 2 1 55 1973 3.54 1
## 79 1787 2 1 38 1973 0.97 0
## 80 1787 2 0 41 1973 1.78 1
## 81 1793 2 0 56 1973 1.94 0
## 82 1804 2 0 48 1973 1.29 0
## 83 1812 2 1 44 1973 3.22 1
## 84 1836 2 0 70 1972 1.53 0
## 85 1839 2 0 40 1972 1.29 0
## 86 1839 2 1 53 1972 1.62 1
## 87 1854 2 0 65 1972 1.62 1
## 88 1856 2 1 54 1972 0.32 0
## 89 1860 3 1 71 1969 4.84 1
## 90 1864 2 0 49 1972 1.29 0
## 91 1899 2 0 55 1972 0.97 0
## 92 1914 2 0 69 1972 3.06 0
## 93 1919 2 1 83 1972 3.54 0
## 94 1920 2 1 60 1972 1.62 1
## 95 1927 2 1 40 1972 2.58 1
## 96 1933 1 0 77 1972 1.94 0
## 97 1942 2 0 35 1972 0.81 0
## 98 1955 2 0 46 1972 7.73 1
## 99 1956 2 0 34 1972 0.97 0
## 100 1958 2 0 69 1972 12.88 0
## 101 1963 2 0 60 1972 2.58 0
## 102 1970 2 1 84 1972 4.09 1
## 103 2005 2 0 66 1972 0.64 0
## 104 2007 2 1 56 1972 0.97 0
## 105 2011 2 0 75 1972 3.22 1
## 106 2024 2 0 36 1972 1.62 0
## 107 2028 2 1 52 1972 3.87 1
## 108 2038 2 0 58 1972 0.32 1
## 109 2056 2 0 39 1972 0.32 0
## 110 2059 2 1 68 1972 3.22 1
## 111 2061 1 1 71 1968 2.26 0
## 112 2062 1 0 52 1965 3.06 0
## 113 2075 2 1 55 1972 2.58 1
## 114 2085 3 0 66 1970 0.65 0
## 115 2102 2 1 35 1972 1.13 0
## 116 2103 1 1 44 1966 0.81 0
## 117 2104 2 0 72 1972 0.97 0
## 118 2108 1 0 58 1969 1.76 1
## 119 2112 2 0 54 1972 1.94 1
## 120 2150 2 0 33 1972 0.65 0
## 121 2156 2 0 45 1972 0.97 0
## 122 2165 2 1 62 1972 5.64 0
## 123 2209 2 0 72 1971 9.66 0
## 124 2227 2 0 51 1971 0.10 0
## 125 2227 2 1 77 1971 5.48 1
## 126 2256 1 0 43 1971 2.26 1
## 127 2264 2 0 65 1971 4.83 1
## 128 2339 2 0 63 1971 0.97 0
## 129 2361 2 1 60 1971 0.97 0
## 130 2387 2 0 50 1971 5.16 1
## 131 2388 1 1 40 1966 0.81 0
## 132 2403 2 0 67 1971 2.90 1
## 133 2426 2 0 69 1971 3.87 0
## 134 2426 2 0 74 1971 1.94 1
## 135 2431 2 0 49 1971 0.16 0
## 136 2460 2 0 47 1971 0.64 0
## 137 2467 1 0 42 1965 2.26 1
## 138 2492 2 0 54 1971 1.45 0
## 139 2493 2 1 72 1971 4.82 1
## 140 2521 2 0 45 1971 1.29 1
## 141 2542 2 1 67 1971 7.89 1
## 142 2559 2 0 48 1970 0.81 1
## 143 2565 1 1 34 1970 3.54 1
## 144 2570 2 0 44 1970 1.29 0
## 145 2660 2 0 31 1970 0.64 0
## 146 2666 2 0 42 1970 3.22 1
## 147 2676 2 0 24 1970 1.45 1
## 148 2738 2 0 58 1970 0.48 0
## 149 2782 1 1 78 1969 1.94 0
## 150 2787 2 1 62 1970 0.16 0
## 151 2984 2 1 70 1969 0.16 0
## 152 3032 2 0 35 1969 1.29 0
## 153 3040 2 0 61 1969 1.94 0
## 154 3042 1 0 54 1967 3.54 1
## 155 3067 2 0 29 1969 0.81 0
## 156 3079 2 1 64 1969 0.65 0
## 157 3101 2 1 47 1969 7.09 0
## 158 3144 2 1 62 1969 0.16 0
## 159 3152 2 0 32 1969 1.62 0
## 160 3154 3 1 49 1969 1.62 0
## 161 3180 2 0 25 1969 1.29 0
## 162 3182 3 1 49 1966 6.12 0
## 163 3185 2 0 64 1969 0.48 0
## 164 3199 2 0 36 1969 0.64 0
## 165 3228 2 0 58 1969 3.22 1
## 166 3229 2 0 37 1969 1.94 0
## 167 3278 2 1 54 1969 2.58 0
## 168 3297 2 0 61 1968 2.58 1
## 169 3328 2 1 31 1968 0.81 0
## 170 3330 2 1 61 1968 0.81 1
## 171 3338 1 0 60 1967 3.22 1
## 172 3383 2 0 43 1968 0.32 0
## 173 3384 2 0 68 1968 3.22 1
## 174 3385 2 0 4 1968 2.74 0
## 175 3388 2 1 60 1968 4.84 1
## 176 3402 2 1 50 1968 1.62 0
## 177 3441 2 0 20 1968 0.65 0
## 178 3458 3 0 54 1967 1.45 0
## 179 3459 2 0 29 1968 0.65 0
## 180 3459 2 1 56 1968 1.29 1
## 181 3476 2 0 60 1968 1.62 0
## 182 3523 2 0 46 1968 3.54 0
## 183 3667 2 0 42 1967 3.22 0
## 184 3695 2 0 34 1967 0.65 0
## 185 3695 2 0 56 1967 1.03 0
## 186 3776 2 1 12 1967 7.09 1
## 187 3776 2 0 21 1967 1.29 1
## 188 3830 2 1 46 1967 0.65 0
## 189 3856 2 0 49 1967 1.78 0
## 190 3872 2 0 35 1967 12.24 1
## 191 3909 2 1 42 1967 8.06 1
## 192 3968 2 0 47 1967 0.81 0
## 193 4001 2 0 69 1967 2.10 0
## 194 4103 2 0 52 1966 3.87 0
## 195 4119 2 1 52 1966 0.65 0
## 196 4124 2 0 30 1966 1.94 1
## 197 4207 2 1 22 1966 0.65 0
## 198 4310 2 1 55 1966 2.10 0
## 199 4390 2 0 26 1965 1.94 1
## 200 4479 2 0 19 1965 1.13 1
## 201 4492 2 1 29 1965 7.06 1
## 202 4668 2 0 40 1965 6.12 0
## 203 4688 2 0 42 1965 0.48 0
## 204 4926 2 0 50 1964 2.26 0
## 205 5565 2 0 41 1962 2.90 0attach(dat)
m = glm(ulcer~time+status+sex+age+year+thickness)
summary(m)##
## Call:
## glm(formula = ulcer ~ time + status + sex + age + year + thickness)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3558 -0.3018 -0.2103 0.4013 0.8430
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.629e+01 2.999e+01 0.543 0.5876
## time -6.429e-05 3.780e-05 -1.701 0.0906 .
## status -1.288e-01 6.368e-02 -2.023 0.0444 *
## sex 6.982e-02 6.491e-02 1.076 0.2834
## age 4.640e-04 1.992e-03 0.233 0.8161
## year -7.971e-03 1.522e-02 -0.524 0.6010
## thickness 5.709e-02 1.154e-02 4.949 1.59e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1948241)
##
## Null deviance: 50.488 on 204 degrees of freedom
## Residual deviance: 38.575 on 198 degrees of freedom
## AIC: 255.33
##
## Number of Fisher Scoring iterations: 2SUMMARY:
(If time increases, ulcer probability ~ 0 decreases 99% OR ulcer probability ~ 1 decreases 1%)
(If status increases, ulcer probability ~ 0 decreases 88% OR ulcer probability ~ 1 decreases 12%)
(If sex = 1, ulcer probability ~ 1 increases 100.7%)
(If age increases, ulcer probability ~ 1 increases 100%)
(If year increases, ulcer probability ~ 0 decreases 100%)
(If thickness increases, ulcer probability ~ 1 increases 105%)
=> All the variables above have approximate impacts on ‘ulcer’.
=> Logistic regression model: ulcer = 16.29 - 0.0000643.time - 0.129.status + 0.0698.sex + 0.000464.age - 0.00797.year + 0.057.thickness
Example: