# R code to analyze the portrait studio data
# using multiple linear regression



# reading the file off the web:
# (This may not work in some implementations of R)

studio.data <- read.table(file = url("http:/www.stat.sc.edu/~hitchcock/stat701/studiodata.txt"), 
header=FALSE, col.names = c('people16', 'income', 'sales'))

# Or, save the data file into a directory and 
# use the full path name:

studio.data <- read.table(file = "y:/My Documents/teaching/stat_701/studiodata.txt", 
header=FALSE, col.names = c('people16', 'income', 'sales'))

# attaching the data frame:

attach(studio.data)

# fitting the regression model:

studio.reg <- lm(sales ~ people16 + income)

# getting the summary regression output:
# (This includes the overall F* = 99.1)

summary(studio.reg)

# getting the ANOVA table:

anova(studio.reg)

# Note that to get the "regression df" and SSR to reflect the SAS 
# ANOVA table, we must add the first two lines together.

# getting the fitted values:

fitted(studio.reg)

# getting the residuals:

resid(studio.reg)

# getting the 95% confidence interval for the mean at X1=65.4 and X2=17.6:

xh.values <- data.frame(cbind(people16 = 65.4, income = 17.6))

predict(studio.reg, xh.values, interval="confidence", level=0.95)

#### Residual plots and other plots ####

# producing the scatter plot matrix

pairs(studio.data)

# residual plot (against fitted values)

plot(fitted(studio.reg), resid(studio.reg), ylab="Residuals", xlab="Fitted Values"); abline(h=0)

# Q-Q plot of residuals

qqnorm(resid(studio.reg))