We have seen hat adding useless predictors to a regression model will increase R2. Here, let's examine what our inference methods say if the predictors are infact 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) # Use this line to make sure we all get the same answes
n = 20
y = 1 + rnorm(n,0,1)
a) write code to make data on 10 useless predictors(and no useful predictors), fit the model y = alpha + beta! 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 - 0.17
c) According to the t-tests, are any of the predictors useful at alpha-0.1? See the solns to make sure you understand the moral of this exercise