Code Challenge 10

\[\newcommand{\E}{\mathbb{E}}\]

For this problem, we’ll use the mtcars data. And in particular, we’ll run the following regression

\[ mpg = \beta_0 + \beta_1 cyl + \beta_2 disp + \beta_3 hp + U \] In class, we talked about using \(AIC\) (Akaike Information Criteria) as a way to choose between different models for prediction. Calculate \(AIC\) for this regression. Hint: \(k\) is equal to 4 in this problem

Rules:

• You cannot load any external packages or call any functions that directly calculate \(AIC\).

To win

• You must email me your code brantly.callaway@uga.edu

• I’ll run exactly the code that you send me, and if your code correctly calculates \(AIC\), then you win.

Solution below…

reg <- lm(mpg ~ cyl + disp + hp, data=mtcars)
Y <- mtcars$mpg
Yhat <- predict(reg)
Uhat <- Y-Yhat
ssr <- sum(Uhat^2)
k <- 4
n <- nrow(mtcars)
aic <- 2*k + n*log(ssr)
aic

## [1] 186.1099