#
# Exercise 12.6
#
# Statistical Methods in Biology: Design and Analysis of Experiments and Regression
# by S.J. Welham, S.A. Gezan, S.J. Clark & A. Mead (2014)
# Chapman & Hall/CRC Press, Boca Raton, Florida. ISBN: 978-1-4398-0878-8
# Data from V. Buchanan-Wollaston (PRESTA), University of Warwick
# Version 1, 15/08/2015

# Set working directory - use setwd() function or from Session menu in RStudio
# e.g. setwd("d:/stats4biol/data)

# Set up packages to be used later - available from CRAN
library(ggplot2)  # for plotting

# Read data 
senescence <- read.table("senescence.dat",sep="",header=T)
summary(senescence)

# Plot CATMA3A13560 against Day
qplot(y=CATMA3A13560, x=Day, data=senescence)

# Fit SLR model 
senescence.slr <- lm(CATMA3A13560~Day, data=senescence)

# Use ANOVA to check for strength of relationship
anova(senescence.slr)

# Summarise using adjusted R-squared
summary(senescence.slr)$adj.r.squared

# Plot residuals
plot(senescence.slr, ask=FALSE)

# Get fitted values and plot with data
fv <- fitted(senescence.slr)
# Set up basic plot using model object
plot.obs <- ggplot(data=senescence.slr, aes(y=CATMA3A13560, x=Day) ) 
# Plot observations and fitted line
plot.obs + geom_point() + geom_line(aes(y=fitted(senescence.slr))) +
  ggtitle("Observed data with fitted SLR")


# SLR model with lack of fit

# Create factor copy of variate Day
senescence$fDay <- as.factor(senescence$Day)
# Fit model with lack of fit
senescence.lof <- lm(CATMA3A13560~Day+fDay, data=senescence)
# ANOVA table indicates lack of fit present
anova(senescence.lof)

# Plot fitted values from the two models with data to interpret lack of fit
senescence.fit <- senescence
senescence.fit$fit.lof <- fitted(senescence.lof)
senescence.fit$fit.slr <- fitted(senescence.slr)
# Set up plot
plot.obs <- ggplot(data=senescence.fit, aes(y=CATMA3A13560, x=Day))
# Plot data, fitted line and fitted means
plot.obs + geom_point() + geom_line(aes(y=fit.slr)) + 
  geom_point(aes(y=fit.lof), colour="red", size=3) +
  ggtitle("Data with fitted means and SLR")

# End of file 

# Note: Exercises 13.1 and 17.2 use different variates from the same data set.