source("http://www.uvm.edu/~rsingle/stat5210/data/scripts-5210.R")

 dat <- otherdata("salary.dat")[,c(3,4,5,7,9)]

#LSTART : log of starting salary
#EDUC   : education years (1-12, 13-16, 17+) 
#SEX    : 0=Male, 1=Female 

#Specifying interactions 
 L.ES   <- lm(LSTART~EDUC+SEX, data=dat)
 inter  <- lm(LSTART~EDUC+SEX + EDUC:SEX, data=dat)
 inter2 <- lm(LSTART~EDUC*SEX, data=dat) #NOTE: * includes all main effects
 inter
 inter2

#Interpreting interactions 
 x0.new.df <- data.frame(EDUC=15, SEX=0) #3 yrs College & Male
 x1.new.df <- data.frame(EDUC=15, SEX=1) #3 yrs College & Female
 predict(inter, x0.new.df) 
 predict(inter, x1.new.df) 
 predict(inter, x0.new.df) - predict(inter, x1.new.df) 

#Assessing confounding 
 EDUC2 <- dat$EDUC^2 
 lm(LSTART ~ EDUC, data=dat)$coef
 lm(LSTART ~ EDUC + EDUC2, data=dat)$coef
 lm(LSTART ~ EDUC + AGE, data=dat)$coef    #no evidence of confounding
 lm(LSTART ~ EDUC + JOBCAT, data=dat)$coef #evidence of confounding
 
 L.A <- lm(LSTART ~ AGE,    data=dat)
 L.J <- lm(LSTART ~ JOBCAT, data=dat)
 E.A <- lm(EDUC   ~ AGE,    data=dat)
 E.J <- lm(EDUC   ~ JOBCAT, data=dat)
 cor(dat$LSTART, dat$EDUC) #r.LE
 cor(L.A$resid, E.A$resid) #r.LE.A
 cor(L.J$resid, E.J$resid) #r.LE.J
 
 YPH <- dat$EDUC-12    #Years Past HS
 lm(LSTART ~ EDUC + YPH, data=dat)$coef
 summary(lm(LSTART ~ EDUC + YPH, data=dat))

 
 
 
 
 
 
 X <- cbind(1,dat$EDUC,YPH)
 inverse(t(X)%*%X) #inverse not possible