###Q2 code

###Plot y vs. x
plot(dat2$x,dat2$y)
abline(lm(y~x, data=dat2))

###Output of first-order model
mod1 <- lm(y~x, data=dat2)
summary(mod1)

###Make residuals plots
plot(fitted(mod1),residuals(mod1))

###Output of second-order model
mod2 <- lm(y~x + I(x^2), data=dat2)
summary(mod2)

###Make residuals plots
plot(fitted(mod2),residuals(mod2))

###Add curve to plot
plot(dat2$x,dat2$y)
x <- dat2$x
curve(mod2$coefficients[1] + mod2$coefficients[2]*x + mod2$coefficients[3]*x^2, from=2, to=16, add=T)

###True model fit
modt <- lm(y ~ x + I(x^2) + w, data=dat2)
summary(modt)