**ERIC Number:**ED219412

**Record Type:**RIE

**Publication Date:**1982-Mar

**Pages:**23

**Abstractor:**N/A

**Reference Count:**0

**ISBN:**N/A

**ISSN:**N/A

On Using the Average Intercorrelation Among Predictor Variables and Eigenvector Orientation to Choose a Regression Solution.

Mugrage, Beverly; And Others

Three ridge regression solutions are compared with ordinary least squares regression and with principal components regression using all components. Ridge regression, particularly the Lawless-Wang solution, out-performed ordinary least squares regression and the principal components solution on the criteria of stability of coefficient and closeness of the beta vector to the population beta vector in this Monte Carlo study. The orientation of the beta vector with respect to the eigenvector associated with the largest eigen value of the X'X matrix was not of significant help in choosing a regression model for particular data varying in multiple correlation coefficient and average absolute intercorrelation among predictor variables. Knowledge of the average absolute intercorrelation among independent variables was used in picking a regression method. For high intercorrelation when stability of regression coefficients is important, ridge regression, particularly Lawless-Wang regression, yielded a superior solution. When stability and accuracy of coefficients is not as important as the accuracy of the predicted Y, the use of ridge regression over ordinary least squares is not indicated. For low average absolute intercorrelation, also, ridge regression solutions did not prove significantly superior to ordinary least squares regression. (Author/PN)

**Publication Type:**Speeches/Meeting Papers; Reports - Research

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers:**Eigenvectors; Principal Components Analysis; Ridge Regression Analysis

**Note:**Paper presented at the Annual Meeting of the American Educational Research Association (66th, New York, NY, March 19-23, 1982).