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Assume we perform least squares linear regression with 2 regularization, with regularization hyper-parameter . For each of the following quantities, explain whether it will increase

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Assume we perform least squares linear regression with 2 regularization, with regularization hyper-parameter . For each of the following quantities, explain whether it will increase or decrease as we increase from 0 up to . You may assume that the optimizer works perfectly, meaning it returns the absolute minimizer of the loss. For each answer, regardless of whether you say increase or decrease, please specify if this holds always or just typically. Don't forget to consider the possibility that some quantities could increase up to a certain value of and then decrease, or vice versa. Please give well reasoned answers. Formal proofs are not required. A: Mean of squared residuals in the training data B: Mean of squared residuals in the test data

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