we will focus on the logistic function.
The logistic function used in logistic regression
data(Carseats)> str(Carseats)
'data.frame': 400 obs. of 11 variables:
$ Sales : num 9.5 11.22 10.06 7.4 4.15 ...
$ CompPrice : num 138 111 113 117 141 124 115 136 132 132 ...
$ Income : num 73 48 35 100 64 113 105 81 110 113 ...
$ Advertising: num 11 16 10 4 3 13 0 15 0 0 ...
$ Population : num 276 260 269 466 340 501 45 425 108 131 ...
$ Price : num 120 83 80 97 128 72 108 120 124 124 ...
$ ShelveLoc : Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
$ Age : num 42 65 59 55 38 78 71 67 76 76 ...
$ Education : num 17 10 12 14 13 16 15 10 10 17 ...
$ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
$ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...
>
> data(Smarke)
Warning message:
In data(Smarke) : data set ‘Smarke’ not found
> data(Smarket)
> str(Smarket)
'data.frame': 1250 obs. of 9 variables:
$ Year : num 2001 2001 2001 2001 2001 ...
$ Lag1 : num 0.381 0.959 1.032 -0.623 0.614 ...
$ Lag2 : num -0.192 0.381 0.959 1.032 -0.623 ...
$ Lag3 : num -2.624 -0.192 0.381 0.959 1.032 ...
$ Lag4 : num -1.055 -2.624 -0.192 0.381 0.959 ...
$ Lag5 : num 5.01 -1.055 -2.624 -0.192 0.381 ...
$ Volume : num 1.19 1.3 1.41 1.28 1.21 ...
$ Today : num 0.959 1.032 -0.623 0.614 0.213 ...
$ Direction: Factor w/ 2 levels "Down","Up": 2 2 1 2 2 2 1 2 2 2 ...
> sales.fit = lm(Sales~Advertising+ShelveLoc, data=Carseats)
>
> summary(sales.fit)
Call:
lm(formula = Sales ~ Advertising + ShelveLoc, data = Carseats)
Residuals:
Min 1Q Median 3Q Max
-6.6480 -1.6198 -0.0476 1.5308 6.4098
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.89662 0.25207 19.426 < 2e-16 ***
Advertising 0.10071 0.01692 5.951 5.88e-09 ***
ShelveLocGood 4.57686 0.33479 13.671 < 2e-16 ***
ShelveLocMedium 1.75142 0.27475 6.375 5.11e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.244 on 396 degrees of freedom
Multiple R-squared: 0.3733, Adjusted R-squared: 0.3685
F-statistic: 78.62 on 3 and 396 DF, p-value: < 2.2e-16
> contrasts(Carseats$ShelveLoc)
Good Medium
Bad 0 0
Good 1 0
Medium 0 1
> contrasts(Carseats$Urban)
Yes
No 0
Yes 1
> contrasts(Carseats$Us)
Error in contrasts(Carseats$Us) : contrasts apply only to factors
> contrasts(Carseats$us)
Error in contrasts(Carseats$us) : contrasts apply only to factors
> contrasts(Carseats$US)
Yes
No 0
Yes 1
> contrasts(Carseats$Price)
Error in contrasts(Carseats$Price) : contrasts apply only to factors
> lm(Today~Lag1+Lag2,data=Smarket)
Call:
lm(formula = Today ~ Lag1 + Lag2, data = Smarket)
Coefficients:
(Intercept) Lag1 Lag2
0.003283 -0.026444 -0.010946
> library("MASS", lib.loc="C:/Program Files/R/R-3.6.1/library")
> data(biopsy)
>
> str(biopsy)
'data.frame': 699 obs. of 11 variables:
$ ID : chr "1000025" "1002945" "1015425" "1016277" ...
$ V1 : int 5 5 3 6 4 8 1 2 2 4 ...
$ V2 : int 1 4 1 8 1 10 1 1 1 2 ...
$ V3 : int 1 4 1 8 1 10 1 2 1 1 ...
$ V4 : int 1 5 1 1 3 8 1 1 1 1 ...
$ V5 : int 2 7 2 3 2 7 2 2 2 2 ...
$ V6 : int 1 10 2 4 1 10 10 1 1 1 ...
$ V7 : int 3 3 3 3 3 9 3 3 1 2 ...
$ V8 : int 1 2 1 7 1 7 1 1 1 1 ...
$ V9 : int 1 1 1 1 1 1 1 1 5 1 ...
$ class: Factor w/ 2 levels "benign","malignant": 1 1 1 1 1 2 1 1 1 1 ...
> biopsy$ID = NULL
>
> names(biopsy) = c("thick", "u.size", "u.shape", "adhsn", "s.size",
+ "nucl", "chrom", "n.nuc", "mit", "class")
>
> names(biopsy)
[1] "thick" "u.size" "u.shape" "adhsn" "s.size" "nucl"
[7] "chrom" "n.nuc" "mit" "class"
>
> biopsy.v2 = na.omit(biopsy)
>
> library("reshape2", lib.loc="~/R/win-library/3.6")
> library("ggplot2", lib.loc="~/R/win-library/3.6")
> biop.m = melt(biopsy.v2, id.var="class")
>
> ggplot(data=biop.m, aes(x=class, y=value)) + geom_boxplot()
> +facet_wrap(~variable,ncol = 3)
Error: Cannot use `+.gg()` with a single argument. Did you accidentally put + on a new line?
>
>
> library("corrplot", lib.loc="~/R/win-library/3.6")
corrplot 0.84 loaded
Warning message:
package ‘corrplot’ was built under R version 3.6.3
> bc = cor(biopsy.v2[ ,1:9])
> corrplot.mixed(bc)
>
> ind = sample(2, nrow(biopsy.v2), replace=TRUE, prob=c(0.7, 0.3))
>
> train = biopsy.v2[ind==1,]
> test = biopsy.v2[ind==2,]
> str(test)
'data.frame': 209 obs. of 10 variables:
$ thick : int 5 6 4 2 1 7 6 7 1 3 ...
$ u.size : int 4 8 1 1 1 4 1 3 1 2 ...
$ u.shape: int 4 8 1 2 1 6 1 2 1 1 ...
$ adhsn : int 5 1 3 1 1 4 1 10 1 1 ...
$ s.size : int 7 3 2 2 1 6 2 5 2 1 ...
$ nucl : int 10 4 1 1 1 1 1 10 1 1 ...
$ chrom : int 3 3 3 3 3 4 3 5 3 2 ...
$ n.nuc : int 2 7 1 1 1 3 1 4 1 1 ...
$ mit : int 1 1 1 1 1 1 1 4 1 1 ...
$ class : Factor w/ 2 levels "benign","malignant": 1 1 1 1 1 2 1 2 1 1 ...
- attr(*, "na.action")= 'omit' Named int 24 41 140 146 159 165 236 250 276 293 ...
..- attr(*, "names")= chr "24" "41" "140" "146" ...
> table(train$class)
benign malignant
302 172
>
> table(test$class)
benign malignant
142 67
>
> full.fit = glm(class~., family=binomial, data=train)
> summary(full.fit)
Call:
glm(formula = class ~ ., family = binomial, data = train)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.3397 -0.1387 -0.0716 0.0321 2.3559
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -9.4293 1.2273 -7.683 1.55e-14
thick 0.5252 0.1601 3.280 0.001039
u.size -0.1045 0.2446 -0.427 0.669165
u.shape 0.2798 0.2526 1.108 0.268044
adhsn 0.3086 0.1738 1.776 0.075722
s.size 0.2866 0.2074 1.382 0.167021
nucl 0.4057 0.1213 3.344 0.000826
chrom 0.2737 0.2174 1.259 0.208006
n.nuc 0.2244 0.1373 1.635 0.102126
mit 0.4296 0.3393 1.266 0.205402
(Intercept) ***
thick **
u.size
u.shape
adhsn .
s.size
nucl ***
chrom
n.nuc
mit
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 620.989 on 473 degrees of freedom
Residual deviance: 78.373 on 464 degrees of freedom
AIC: 98.373
Number of Fisher Scoring iterations: 8
>
> confint(full.fit)
Waiting for profiling to be done...
2.5 % 97.5 %
(Intercept) -12.23786660 -7.3421509
thick 0.23250518 0.8712407
u.size -0.56108960 0.4212527
u.shape -0.24551513 0.7725505
adhsn -0.02257952 0.6760586
s.size -0.11769714 0.7024139
nucl 0.17687420 0.6582354
chrom -0.13992177 0.7232904
n.nuc -0.03813490 0.5110293
mit -0.14099177 1.0142786
> exp(coef(full.fit))
(Intercept) thick u.size
8.033466e-05 1.690879e+00 9.007478e-01
u.shape adhsn s.size
1.322844e+00 1.361533e+00 1.331940e+00
nucl chrom n.nuc
1.500309e+00 1.314783e+00 1.251551e+00
mit
1.536709e+00
>
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