**APPENDIX 1**

**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 β_{i}, is found and set to zero. ...

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