mtcars # data on cars

# Is fuel efficiency better for manual transmission cars (am=1)?
t.test(mpg ~ factor(am), mtcars)

mpg ~ factor(gear)

g <- as.numeric(factor(mtcars$gear))
X <- cbind(1, as.numeric(g == 1), as.numeric(g == 2), as.numeric(g == 3))

## or, more simply

X <- cbind(1, diag(length(unique(g)))[g, ])



for (nm in c("cyl", "vs", "am", "gear", "carb"))
    mtcars[[ nm ]] <- as.factor(mtcars[[ nm ]])
str(mtcars)

## This actually makes a copy of 'mtcars' in the global environment
find("mtcars")
str(datasets::mtcars) # unchanged

model.matrix(mpg ~ gear, data = mtcars)

model.matrix(mpg ~ gear, data = mtcars,
             contrasts.arg = list(gear = contr.SAS))

model.matrix(mpg ~ gear, data = mtcars,
             contrasts.arg = list(gear = contr.poly))

model.matrix(mpg ~ gear, data = mtcars,
             contrasts.arg = list(gear = contr.helmert))



fm1 <- lm(mpg ~ gear, data = mtcars)
summary(fm1)
anova(fm1)

fm2 <- lm(mpg ~ gear + cyl, data = mtcars)
summary(fm2)
anova(fm2)

fm3 <- lm(mpg ~ cyl + gear, data = mtcars)
summary(fm3)
anova(fm3)

drop1(fm2)

boxplot(mpg ~ cyl, mtcars)
boxplot(mpg ~ gear, mtcars)

## Regression models

fm4 <- lm(mpg ~ disp, data = mtcars)
summary(fm4)
anova(fm4)

plot(mpg ~ disp, data = mtcars)
plot(mpg ~ wt, data = mtcars)

fm5 <- lm(mpg ~ disp + wt, data = mtcars)
summary(fm5)
anova(fm5)

fm6 <- lm(mpg ~ wt + disp, data = mtcars)
summary(fm6)
anova(fm6)

fm7 <- lm(mpg ~ gear + wt + disp, data = mtcars)
summary(fm7)
anova(fm7)

## Simpler model with one numeric and one categorical variable

fm8 <- lm(mpg ~ gear + wt, data = mtcars)
plot(mpg ~ wt, mtcars, col = mtcars$gear)
coef(fm8)
abline(coef(fm8)[1], coef(fm8)["wt"], col = 1)
abline(coef(fm8)[1] + coef(fm8)[2], coef(fm8)["wt"], col = 2)
abline(coef(fm8)[1] + coef(fm8)[3], coef(fm8)["wt"], col = 3)


fm9 <- lm(mpg ~ gear + wt + gear:wt, data = mtcars)
fm9 <- lm(mpg ~ gear * wt, data = mtcars)
plot(mpg ~ wt, mtcars, col = mtcars$gear)
cc <- coef(fm9)
abline(cc[1], cc[4], col = 1)
abline(cc[1] + cc[2], cc[4] + cc[5], col = 2)
abline(cc[1] + cc[3], cc[4] + cc[6], col = 3)

summary(fm9)
anova(fm9)

fm9 <- lm(mpg ~ gear:wt + gear + wt, data = mtcars)