# R code to analyze the cornmeal data
# using polynomial regression

# In this data set (taken from Spurrier 
# (1993, Technometrics)), the response 
# is the diameter of a cornmeal product 
# and the predictor is the percent of 
# sucrose in the product.            



# Save the data file into a directory and 
# use the full path name:

cornmeal.data <- read.table(file = "z:/My Documents/teaching/stat_704/cornmealdata.txt", 
header=FALSE, col.names = c('sucrpct', 'diameter'))

# attaching the data frame:

attach(cornmeal.data)

# Scatterplot to check the shape of the regression relationship:

plot(sucrpct, diameter)

# Centering the X variable and
# creating a quadratic term:

csucrpct <- sucrpct - mean(sucrpct);
csucrpctsq <- csucrpct^2;

# fitting the regression model:

corn.reg <- lm(diameter ~ csucrpct + csucrpctsq)

# getting the summary regression output:
# (This includes the overall F* = 15.41)

summary(corn.reg)

# getting the ANOVA table:

anova(corn.reg)

# Plotting the fitted regression curve with the data (naive approach):

plot(sucrpct, diameter); lines(sucrpct, fitted(corn.reg))

# A better way to plot, but more complicated:

xgrid <- seq(from=min(csucrpct), to=max(csucrpct), length=100)
predgrid <- cbind(rep(1,times=length(xgrid)), xgrid, xgrid^2) %*% corn.reg$coef
plot(sucrpct, diameter); lines(xgrid + mean(sucrpct), predgrid)