Unformatted text preview: STAT 100B HWV Due Friday
Problem 1: Suppose we want to ﬁt the linear regression model yi = xi1 β1 + xi2 β2 + ... + xip βp + i for i = 1, 2, ..., n by the least squares principle, i.e., we estimate β = (β1 , β2 , ..., βp )T by minimizing
n n i=1 R(β ) =
i=1 [yi − (xi1 β1 + xi2 β2 + ... + xip βp )]2 = (yi − xT β )2 , i where xi = (xi1 , xi2 , ..., xip )T . ˆ (1) Calculate the least squares estimate β . (2) Compare the result in (1) with the result we obtained before for p = 1. (3) Compare the result in (1) with the result we obtained before for simple linear regression with the intercept. 1 ...
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