We have two person. Person 1 trained the Linear Regression model that produces +0.5 deviation from the true value on 400 test samples and -0.7 deviation from true value on the rest 100 test samples (500 in total). First question is what MSE does this person has? I've calculated it as 1 / 500 * (400 * (0.5)^2 + 100 * (-0.7)^2) = 0.298
But the Person 2 claims that it's possible to use a constant model that will produce the better result. What would be his error? I've stuck on the second problem, because it seems like we need to always predict the mean value to minimize the MSE for the constant model. This way RMSE would be equal the standard deviation of the vector with true values and hence MSE would be standard deviation squared. But the result is expected to be the actual number and I'm not sure how it's possible to calculate here. Maybe we need to somehow use the deviations from the Person 1, but I have no idea how they can be helpful for MSE of the constant model. Any guidance will be appreciated.