# Scott Merrill
# Oct 16
# Quantitative Thinking
# Cow weight

rm(list = ls(all = TRUE))


###########
# generating a line with error
###########

outflow.nitrogen = sample(0:60,100,replace = TRUE)
data.error = rnorm(n=100,mean=0,sd=4)

slope = .075
cow.weight = outflow.nitrogen*slope + data.error

plot(outflow.nitrogen,cow.weight, main = "Amount of Nitrogen in overland irrigation outflow vs 
Percent change in cow weight by field")


mod1= glm(cow.weight~outflow.nitrogen + data.error)
summary(mod1)

#fitted line
abline(mod1$coefficients, lwd = 4, col = "green")

# zero line
abline(0,0, lwd = 4, col = "red")

# plot distances
plot(cow.weight, col = "red", lwd = 2)
points(mod1$residuals, col = "green", lwd = 2)
abline(0,0, lwd = 4, col = "black")

# plot sorted distances
plot(sort(cow.weight), col = "red", lwd = 2)
points(sort(mod1$residuals), col = "green", lwd = 2)
abline(0,0, lwd = 4, col = "black")

# statistically speaking we care about the squared error
error.zero.line = cow.weight^2
sum(error.zero.line)

error.fit.line = mod1$residuals^2
sum(error.fit.line)

# plotting the squared error
plot(sort(error.zero.line), col = "red")
points(sort(error.fit.line), col ="green")
abline(0,0, lwd = 4, col = "black")

summary(mod1)

mtext(c("F-statistic, DF model, DF error
",summary(mod1)[10]), line = -20, side = 1)