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Let X in R and Y in R be the input and output random variables andletY =X+, where ~N(0,^2)be a linear regression model that we
Let X in R and Y in R be the input and output random variables andletY =X+, where ~N(0,^2)be a linear regression model that we are working with. Given n i.i.d. training copies (x1, y1), . . . , (xn, yn) of (X, Y ), let be the standard least-squares estimator of . Let c > 0 be a constant. Now suppose that, we scale each input sample xi by c (i.e., we use cxi instead of xi during training) with the output samples remaining the same. Derive the new least-squares solution when using the scaled data and represent the new solution in terms of ^
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