Question

We have seen that adding useless predictors to a regression model will increase R2. Here, let's examine what our inference methods say if the predictors are in fact useless. Suppose the true/pop fit is y = 1,(i.e., no x at all), and so a possible sample from the population could be the following:

set.seed(123)

n = 20

y = 1 + rnorm(n,0,1)

a) Write code to make data on 10 useless predictors (and no useful predictors) each from unif(-1,+1), fit the model y = alpha + beta1 x1 + ... + beta10 x10, perform the test of model utility, and perform t-tests on each of the 10 coefficients to see if they are zero. Show/turn-in your R code.

b) According to the F-test of model utility, are any of the predictors useful at alpha = 0.1?

c) According to the t-tests, are any of the predictors useful at alpha = 0.1?

Answer 1