The Mathematical Basis for Multiple Regression/Correlation and Identification of the Inverse Matrix Elements
The OLS regression model requires the determination of a set of weights for the k independent variables that, when used in the linear regression equation, minimizes the average squared deviation of the estimated Ŷ scores from the Y scores. This solution is somewhat simplified by standardizing all variables. Thus the problem is to find a set of β weights such that
is a minimum, as we have seen. By means of the differential calculus, the partial derivative of the function with respect to each unknown βi, is found and set to zero. ...