# EXAMPLE CODE FOR REGRESSION & AOV
# read in data
x<-c(20,16,34,23,27,32,18,22)
y<-c(64,61,84,70,88,92,72,77)
mymodel <- lm(y~x) # run regression model
summary(mymodel) # output
dat1 <- data.frame(x,y) # combine x and y into an R data frame
ss <- aov(y~x, data = dat1) # conduct analysis of variance & save results as 'ss'
summary(ss) # print results
# to read the output you must realize that the row 'x' gives you the SSR & MSR
# the row 'Residuals' gives tyou SSE & MSE
# SST is not given but you know the formula to get it SST = SSR + SSE
# based on output, calculate SST = SSR + SSE
SST <- 658.5 + 227.5
print(SST) # this gives you SST
# use this info to calculate R-square = SSR / SST
658.5/SST # gives .743 which was given in the original regression output
# verify that the F- stat is MSR / MSE based on the output from summary(ss)
F<- 658.5/37.92
print(F) # this gives the same results as summary(ss)
