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In forward stepwise regression, what advantage is there in using a relatively small alpha-to-enter value for adding variables? What advantage is there in using a larger alpha-to-enter value?
I've been stuck on this problem for the last two days. If anyone could help, it would be greatly appreciated!
Use the following two matrix rules to show that if n=p and the X matrix is invertible, the hat matrix H is given by the p x p identity matrix.
(1) (AB)^-1 = B^-1 * A^-1
(2) (A')^-1 = (A^-1)', where ' means "transpose"
Consider a coin for which the probability of obtaining a head on each given toss is 0.3. Suppose that the coin is to be tossed 15 times, and let X denote the number of heads that will be obtained.
a) What prediction of X has the smallest mean square error (MSE)?
b) What prediction of X has the smallest mean absolute error (MAE)?
Now for part a, if I am correct, the prediction of X that has the smallest mean square error is just the variance np(1-p) = 3.15 because this is a binomial distribution with parameters n=15 and p=.3.
But I am puzzled as to how to find the prediction of X with the smallest mean absolute error. If anyone could explain, I would really appreciate it!
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