#
# Exercise 12.2
#
# 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 R Harrington & C Shortall, Rothamsted Research
# Version 1, 14/08/2015

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

# Get log transformation of wet weights
hereford$logWt <- log10(hereford$WetWeight+0.5)

# Plot data
qplot(y=logWt, x=Year, data=hereford)

# Fit SLR model 
hereford.slr <- lm(logWt~Year, data=hereford)

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

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

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

# Regression model parameter estimates
summary(hereford.slr)$coefficients

# Prediction for 2010 - extrapolation!
hereford.pred.slr <- predict(hereford.slr, new=data.frame(Year=c(2010)), 
                             interval="confidence", se.fit=TRUE)
hereford.pred.slr$fit
hereford.pred.slr$se.fit

# Back-transform predictions
hereford.pred.back <- (10^hereford.pred.slr$fit)-0.5
hereford.pred.back

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

# Look for temporal correlation
res <- residuals(hereford.slr)
nv <- length(res)
nvm1 <- nv-1
# correlation between residual and residual from previous year
cor(res[1:nvm1],res[2:nv])
# plot residual vs that from previous year
plot(y=res[1:nvm1],x=res[2:nv])
# plot residuals across time
plot(y=res,x=hereford$Year,type='b')

# End of file - but see also Exercises 13.4 and 15.1