############################################
#Aiken, L. S., & West, S. G. (1991).
#Interactions between categorical and continuous variables
#In Multiple Regression: Testing and interpreting interactions (pp.116-138).
#Thousand Oaks: Sage.
############################################

##(a) データの読み込み (Table 7.2)
dat <- read.csv("http://blue.zero.jp/yokumura/R/reg/Aiken.csv",header=T)
dat

dat$college <- factor(dat$college,levels=c("LA","E","BUS"))
attach(dat)
        tapply(salary,college,mean)
        tapply(GPA,college,mean)


##(b) Categorical Variable Only p.118-119
        reg1 <- lm(salary~college)
        summary(reg1)                              #Joint test of b_1, b_2
        anova(reg1)                                #SSreg, SSres
        
        par(mfrow=c(2,2))
        plot(salary~GPA,type="n",ylim=c(0,max(salary)), main="Figure 7.1a")
        abline(h=c(tapply(salary,college,mean)),lty=1:3,col=2:4)
        legend(3,20000,levels(college),lty=1:3,col=2:4)


##(c) Categorical and Continuous Variable p.119-123
        cGPA <- GPA-mean(GPA)			#centering
        reg2 <- lm(salary~college+cGPA)         #eq7.2
        summary(reg2)
        anova(reg1, reg2)
        anova(reg2)

        coef1 <- coef(reg2)
        plot(salary~cGPA,type="n",xlim=c(-2.78,1.22),ylim=c(0,max(salary)*1.1))
        abline(c(coef1[1],          coef1[4]),          lty=1,col=2)
        abline(c(coef1[1]+coef1[2], coef1[4]),          lty=2,col=3)
        abline(c(coef1[1]+coef1[3], coef1[4]),          lty=3,col=4)
        legend(0,20000,levels(college),lty=1:3,col=2:4)


##(d) Categorical and Continuous Variables and their Interaction p.123-126
        reg3 <- lm(salary~college*cGPA)
        summary(reg3)
        anova(reg2, reg3)
        anova(reg3)
        
        coef2 <- coef(reg3)
        plot(salary~cGPA,type="n",xlim=c(-2.78,1.22),ylim=c(0,max(salary)*1.1))
        abline(c(coef2[1],           coef2[4]         ),lty=1,col=2)
        abline(c(coef2[1]+coef2[2],  coef2[4]+coef2[5]),lty=2,col=3)
        abline(c(coef2[1]+coef2[3],  coef2[4]+coef2[6]),lty=3,col=4)
        legend(0,20000,levels(college),lty=1:3,col=2:4)

        graphics.off()

detach(dat)