# R example of lack of fit test

# The data are from the bank example discussed in class.

# deposit will be our predictor variable (X).
# accounts will be our response variable (Y).

# Reading the data into R:

my.datafile <- tempfile()
cat(file=my.datafile, "
  125  160
  100  112
  200  124
   75   28
  150  152
  175  156
   75   42
  175  124
  125  150
  200  104
  100  136
", sep=" ")

options(scipen=999) # suppressing scientific notation

banks <- read.table(my.datafile, header=FALSE, col.names=c("deposit","accounts")) 
  
attach(banks)

#########

#########

## Initial scatterplot of data:

plot(deposit, accounts)

# Not a linear trend?

# Reduced (linear) model
reduced_model_37 <- lm(accounts ~ deposit, data = banks)

# Full (categorical/factor) model
full_model_37 <- lm(accounts ~ factor(deposit), data = banks)

# Compare models with ANOVA (general linear test)
anova(reduced_model_37, full_model_37)

# Find the results of the lack-of-fit F-test in the R output.

# Compare the results in the R output to the results in the
# book (Sec. 3.7) for the banks example.