Question: The least squares prediction equation provides predicted values yn with the strongest possible correlation with y, out of all possible prediction equations of that form.

The least squares prediction equation provides predicted values yn with the strongest possible correlation with y, out of all possible prediction equations of that form. Based on this property, explain why the multiple correlation R cannot decrease when you add a variable to a multiple regression model. (Hint: The prediction equation for the simpler model is a special case of a prediction equation for the full model that has coefficient 0 for the added variable.)

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