The ordinary least-squares method of regression analysis is based on the logic of how much better a regression line can predict values of Y compared to simply using the mean as a prediction.

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The ordinary least-squares method of regression analysis aims to minimize the sum of the squared differences between the predicted values of Y and the actual values of Y. This is compared to simply using the mean as a prediction, which does not take into account any relationship between X and Y. Therefore, the OLS regression line should be able to predict values of Y better than using just the mean.

The Ordinary Least-Squares Method of Regression Analysis Is Based on the Logic