# File: Regression.R
# Course: ENG7218: Health Data Science
# INSTALL AND LOAD PACKAGES ################################
library(datasets) # Load base packages manually
# Installs pacman ("package manager") if needed
if (!require("pacman")) install.packages("pacman")
## Loading required package: pacman
## Warning: package 'pacman' was built under R version 4.3.3
# Use pacman to load add-on packages as desired
pacman::p_load(pacman, caret, lars, tidyverse)
# LOAD DATA ################################################
?USJudgeRatings
## starting httpd help server ...
## done
head(USJudgeRatings)
## CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL WRIT PHYS RTEN
## AARONSON,L.H. 5.7 7.9 7.7 7.3 7.1 7.4 7.1 7.1 7.1 7.0 8.3 7.8
## ALEXANDER,J.M. 6.8 8.9 8.8 8.5 7.8 8.1 8.0 8.0 7.8 7.9 8.5 8.7
## ARMENTANO,A.J. 7.2 8.1 7.8 7.8 7.5 7.6 7.5 7.5 7.3 7.4 7.9 7.8
## BERDON,R.I. 6.8 8.8 8.5 8.8 8.3 8.5 8.7 8.7 8.4 8.5 8.8 8.7
## BRACKEN,J.J. 7.3 6.4 4.3 6.5 6.0 6.2 5.7 5.7 5.1 5.3 5.5 4.8
## BURNS,E.B. 6.2 8.8 8.7 8.5 7.9 8.0 8.1 8.0 8.0 8.0 8.6 8.6
data <- USJudgeRatings
# Define variable groups
x <- as.matrix(data[, -12])
y <- data[, 12]
# REGRESSION WITH SIMULTANEOUS ENTRY #######################
# Using variable groups
reg1 <- lm(y ~ x)
# Or specify variables individually
reg1 <- lm(RTEN ~ CONT + INTG + DMNR + DILG + CFMG +
DECI + PREP + FAMI + ORAL + WRIT + PHYS,
data = USJudgeRatings)
# Results
reg1 # Coefficients only
##
## Call:
## lm(formula = RTEN ~ CONT + INTG + DMNR + DILG + CFMG + DECI +
## PREP + FAMI + ORAL + WRIT + PHYS, data = USJudgeRatings)
##
## Coefficients:
## (Intercept) CONT INTG DMNR DILG CFMG
## -2.11943 0.01280 0.36484 0.12540 0.06669 -0.19453
## DECI PREP FAMI ORAL WRIT PHYS
## 0.27829 -0.00196 -0.13579 0.54782 -0.06806 0.26881
summary(reg1) # Inferential tests
##
## Call:
## lm(formula = RTEN ~ CONT + INTG + DMNR + DILG + CFMG + DECI +
## PREP + FAMI + ORAL + WRIT + PHYS, data = USJudgeRatings)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.22123 -0.06155 -0.01055 0.05045 0.26079
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.11943 0.51904 -4.083 0.000290 ***
## CONT 0.01280 0.02586 0.495 0.624272
## INTG 0.36484 0.12936 2.820 0.008291 **
## DMNR 0.12540 0.08971 1.398 0.172102
## DILG 0.06669 0.14303 0.466 0.644293
## CFMG -0.19453 0.14779 -1.316 0.197735
## DECI 0.27829 0.13826 2.013 0.052883 .
## PREP -0.00196 0.24001 -0.008 0.993536
## FAMI -0.13579 0.26725 -0.508 0.614972
## ORAL 0.54782 0.27725 1.976 0.057121 .
## WRIT -0.06806 0.31485 -0.216 0.830269
## PHYS 0.26881 0.06213 4.326 0.000146 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1174 on 31 degrees of freedom
## Multiple R-squared: 0.9916, Adjusted R-squared: 0.9886
## F-statistic: 332.9 on 11 and 31 DF, p-value: < 2.2e-16
# MORE SUMMARIES ###########################################
anova(reg1) # Coefficients w/inferential tests
## Analysis of Variance Table
##
## Response: RTEN
## Df Sum Sq Mean Sq F value Pr(>F)
## CONT 1 0.058 0.058 4.1794 0.0494903 *
## INTG 1 45.096 45.096 3270.7650 < 2.2e-16 ***
## DMNR 1 1.300 1.300 94.3167 6.415e-11 ***
## DILG 1 2.346 2.346 170.1567 3.963e-14 ***
## CFMG 1 0.503 0.503 36.5172 1.086e-06 ***
## DECI 1 0.214 0.214 15.5296 0.0004306 ***
## PREP 1 0.164 0.164 11.9069 0.0016353 **
## FAMI 1 0.039 0.039 2.7997 0.1043449
## ORAL 1 0.439 0.439 31.8608 3.385e-06 ***
## WRIT 1 0.065 0.065 4.7078 0.0378096 *
## PHYS 1 0.258 0.258 18.7170 0.0001464 ***
## Residuals 31 0.427 0.014
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coef(reg1) # Coefficients (same as reg1)
## (Intercept) CONT INTG DMNR DILG CFMG
## -2.119429682 0.012796377 0.364840272 0.125399138 0.066690976 -0.194527027
## DECI PREP FAMI ORAL WRIT PHYS
## 0.278292932 -0.001960111 -0.135790972 0.547817680 -0.068061595 0.268811919
confint(reg1) # CI for coefficients
## 2.5 % 97.5 %
## (Intercept) -3.178010347 -1.06084902
## CONT -0.039955335 0.06554809
## INTG 0.101011150 0.62866939
## DMNR -0.057571651 0.30836993
## DILG -0.225031708 0.35841366
## CFMG -0.495940888 0.10688683
## DECI -0.003683181 0.56026904
## PREP -0.491456059 0.48753584
## FAMI -0.680844080 0.40926214
## ORAL -0.017628284 1.11326364
## WRIT -0.710196975 0.57407378
## PHYS 0.142088434 0.39553540
resid(reg1) # Residuals case-by-case
## AARONSON,L.H. ALEXANDER,J.M. ARMENTANO,A.J. BERDON,R.I. BRACKEN,J.J.
## 0.1674282950 0.1599043028 0.1318188003 -0.0721243488 -0.1663513584
## BURNS,E.B. CALLAHAN,R.J. COHEN,S.S. DALY,J.J. DANNEHY,J.F.
## 0.0344455088 -0.1228672774 -0.0359845065 -0.0414643393 0.1054849167
## DEAN,H.H. DEVITA,H.J. DRISCOLL,P.J. GRILLO,A.E. HADDEN,W.L.JR.
## 0.0315661299 0.0279048490 -0.0066302844 0.1215116258 -0.0707169455
## HAMILL,E.C. HEALEY.A.H. HULL,T.C. LEVINE,I. LEVISTER,R.L.
## 0.0963751277 0.0966781231 0.0587324090 0.2607914304 -0.0613783951
## MARTIN,L.F. MCGRATH,J.F. MIGNONE,A.F. MISSAL,H.M. MULVEY,H.M.
## -0.0105476010 -0.0926140135 -0.0964022149 -0.0479617600 0.0279999236
## NARUK,H.J. O'BRIEN,F.J. O'SULLIVAN,T.J. PASKEY,L. RUBINOW,J.E.
## -0.0633662511 -0.0142423076 -0.1918226956 0.0253091922 -0.0179725262
## SADEN.G.A. SATANIELLO,A.G. SHEA,D.M. SHEA,J.F.JR. SIDOR,W.J.
## -0.0144131915 0.1145104470 -0.0617147925 -0.0608608820 0.0421019215
## SPEZIALE,J.A. SPONZO,M.J. STAPLETON,J.F. TESTO,R.J. TIERNEY,W.L.JR.
## 0.1474606096 0.0421784997 -0.2212325911 -0.0375263260 -0.0007537799
## WALL,R.A. WRIGHT,D.B. ZARRILLI,K.J.
## -0.0024277845 -0.1204656347 -0.0603603048
hist(residuals(reg1)) # Histogram of residuals
# ADDITIONAL MODELS ########################################
# Conventional stepwise regression
stepwise <- lars(x, y, type = "stepwise")
# Stagewise: Like stepwise but with better generalizability
forward <- lars(x, y, type = "forward.stagewise")
# LAR: Least Angle Regression
lar <- lars(x, y, type = "lar")
# LASSO: Least Absolute Shrinkage and Selection Operator
lasso <- lars(x, y, type = "lasso")
# Comparison of R^2 for new models
r2comp <- c(stepwise$R2[6], forward$R2[6],
lar$R2[6], lasso$R2[6]) %>%
round(2)
names(r2comp) <- c("stepwise", "forward", "lar", "lasso")
r2comp # Show values of R^2
## stepwise forward lar lasso
## 0.99 0.99 0.99 0.99
# CLEAN UP #################################################
# Clear environment
rm(list = ls())
# Clear packages
p_unload(all) # Remove all add-ons
## The following packages have been unloaded:
## lubridate, forcats, stringr, dplyr, purrr, readr, tidyr, tibble, tidyverse, lars, caret, lattice, ggplot2, pacman
detach("package:datasets", unload = TRUE) # For base
# Clear plots
dev.off() # But only if there IS a plot
## null device
## 1
# Clear console
cat("\014") # ctrl+L
# Clear mind :)