Question: Consider a multiple linear regression problem with design matrix Z and observations Y. Let Z1 be the matrix remaining when at least one column is

Consider a multiple linear regression problem with design matrix Z and observations Y. Let Z1 be the matrix remaining when at least one column is removed from Z. Then Z1 is the design matrix for a linear regression problem with fewer predictors and the same data Y. Prove that the value of R2 calculated in the problem using design matrix Z is at least as large as the value of R2 calculated in the problem using design matrix Z1.

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