Description

Saket Choudhary (USCID: 2170058637) (skchoudh@usc.edu)
Chapter 12: 14
require(leaps)
## Loading required package: leaps
data <- read.csv(‘case1102.csv’) data$logY = log(data$Brain/data$Liver)
Y <- data$logY
X <- data[,c(‘Days’, ‘Sex’, ‘Weight’, ‘Loss’, ‘Tumor’)]
We use the leaps package to perform subset selection.
rsubsets <- regsubsets(logY ~ Days+Sex+Weight+Loss+Tumor, data=data)
s <- summary(rsubsets, matrix.logical=TRUE) s$cp
## [1] 9.457598 1.430200 2.006538 4.000835 6.000000
Part (a): Cp
plot(rsubsets, scale=’Cp’)

The way to interpet this plot is to look at first the smallest Cp values, which happens to be around 1.4 and see the black dots which in this case are given by Days, SexMale So if we were to choose the covarates based only on Cp values, we select: Days and Sex Here p = 5 and in principle any model with Cp < p is better than the full model, so we can also select these:
• Days, Sex: Cp = 1.43
• Days, Sex, Weight: Cp = 2.006
• Days, Sex, Weight, Tumor: Cp = 4.00008
Part (b): Forward Selection
rsubsets <- regsubsets(logY ~ Days+Sex+Weight+Loss+Tumor,
data=data, method=’forward’)
sforward <- summary(rsubsets, matrix.logical=TRUE) sforward
## Subset selection object
## Call: regsubsets.formula(logY ~ Days + Sex + Weight + Loss + Tumor,
## data = data, method = “forward”)
## 5 Variables (and intercept)
## Forced in Forced out ## Days FALSE FALSE ## SexMale FALSE FALSE ## Weight FALSE FALSE ## Loss FALSE FALSE ## Tumor FALSE FALSE
## 1 subsets of each size up to 5
## Selection Algorithm: forward
## Days SexMale Weight Loss Tumor ## 1 ( 1 ) FALSE TRUE FALSE FALSE FALSE ## 2 ( 1 ) TRUE TRUE FALSE FALSE FALSE ## 3 ( 1 ) TRUE TRUE TRUE FALSE FALSE ## 4 ( 1 ) TRUE TRUE TRUE FALSE TRUE
## 5 ( 1 ) TRUE TRUE TRUE TRUE TRUE
Part (c): Backward Selection
rsubsets <- regsubsets(logY ~ Days+Sex+Weight+Loss+Tumor,
data=data, method=’backward’)
sbackward <- summary(rsubsets, matrix.logical=TRUE) sbackward
## Subset selection object
## Call: regsubsets.formula(logY ~ Days + Sex + Weight + Loss + Tumor,
## data = data, method = “backward”)
## 5 Variables (and intercept)
## Forced in Forced out
## Days FALSE FALSE ## SexMale FALSE FALSE ## Weight FALSE FALSE ## Loss FALSE FALSE ## Tumor FALSE FALSE
## 1 subsets of each size up to 5
## Selection Algorithm: backward
## Days SexMale Weight Loss Tumor ## 1 ( 1 ) FALSE TRUE FALSE FALSE FALSE ## 2 ( 1 ) TRUE TRUE FALSE FALSE FALSE ## 3 ( 1 ) TRUE TRUE TRUE FALSE FALSE ## 4 ( 1 ) TRUE TRUE TRUE FALSE TRUE
## 5 ( 1 ) TRUE TRUE TRUE TRUE TRUE
Part(d): Stepwise Regression
rsubsets <- regsubsets(logY ~ Days+Sex+Weight+Loss+Tumor,
data=data, method=”seqrep”)
sboth <- summary(rsubsets, matrix.logical=TRUE) sboth
## Subset selection object
## Call: regsubsets.formula(logY ~ Days + Sex + Weight + Loss + Tumor,
## data = data, method = “seqrep”)
## 5 Variables (and intercept)
## Forced in Forced out ## Days FALSE FALSE ## SexMale FALSE FALSE ## Weight FALSE FALSE ## Loss FALSE FALSE ## Tumor FALSE FALSE
## 1 subsets of each size up to 5
## Selection Algorithm: ‘sequential replacement’
## Days SexMale Weight Loss Tumor ## 1 ( 1 ) FALSE TRUE FALSE FALSE FALSE ## 2 ( 1 ) TRUE TRUE FALSE FALSE FALSE ## 3 ( 1 ) TRUE TRUE TRUE FALSE FALSE ## 4 ( 1 ) TRUE TRUE TRUE FALSE TRUE
## 5 ( 1 ) TRUE TRUE TRUE TRUE TRUE
Conclusion
From the above, we conclude that the variable selection in this case gives us the same set for all four methods.