if( !require('investr') ){
    install.packages('investr', dependencies=TRUE, repos='http://cran.rstudio.com/')
}
library(investr) # has the function plotFit

load(file='../../BookCode/nlrwr/data/vapCO.rda')
plot(vapCO$T, log(vapCO$p), xlab='Temperature (K)', ylab='log(Pressure (Pa))')
grid()

vapCO.m1 = nls(log(p) ~ A - B/T, data=vapCO, start=list(A=10, B=100))
print(summary(vapCO.m1))

# Now that we have a model, lets study the fitting assumptions following the steps discussed in this chapter of the book:
#
plotFit(vapCO.m1, main='vapCO data and fit')
grid()

# Residual plot:
#
plot(fitted(vapCO.m1), residuals(vapCO.m1), xlab='fitted values', ylab='residuals')
abline(h=0, col='black')
grid()

# F-test:
#
n = dim(vapCO)[1]
nc = length(unique(vapCO$T))
if( nc < n ){ # we must have repeated measurements
    print('F-test')
    full_model = lm(log(p) ~ as.factor(T), data=vapCO)
    print(anova(vapCO.m1, full_model))
}

# Variance homogeneity:
#
plot(fitted(vapCO.m1), abs(residuals(vapCO.m1)), xlab='fitted values', ylab='abs residuals')
grid()

# Normality of the residuals:
#
standardRes = residuals(vapCO.m1)/summary(vapCO.m1)$sigma
qqnorm(standardRes, main='')
abline(a=0, b=1)
grid()

print(shapiro.test(standardRes))

# Independence:
#
#plot(residuals(vapCO.m1), c(residuals(vapCO.m1)[-1], NA), xlab='residuals', ylab='lagged residuals')
#grid()
acf(residuals(vapCO.m1))