Multiple Regression Analysis

Summary of the Most Inportant Items Contained on Output

Under the heading Model Summary:

R is the multiple correlation between the dependent variable and the combined independent variables.

R square represents the percentage of variance in the dependent variable which is accounted for by the independent variables.

Adjusted R square represents the percentage of variance in the dependent variable which is accounted for by the independent variables adjusted for sample size.

The standard error of estimate represents the standard deviation of the residuals, and is a measure of the accuracy of the prediction ability of the equation. This value may range from 0 to the standard deviation of the dependent variable.

R square change is the proportion of variance in the dependent variable which is accounted for by the variable added to the equation in the current step.

Sig F. Change  indicates whether the equation or the multiple correlation itself is significant. When Stepwise mode is used, this will determine whether the variable added at each step significantly improved the correlation.  In order to be considered significant, the p value must be less than 0.05, or the chosen alpha level.

F change and Sig. F Change indicate whether the model provides significantly better estimates compared to using only the mean (when Enter is the mode used for the model) or, whether themodel provides significantly better estimates when each new variable is added to the equation (when Stepwise is the mode used for the model).

Durbin-Watson indicates whether the assumption of uncorrelated residuals has been met. As a rule of thumb, this number should be between 1-3 to consider the residuals uncorrelated.

B, also referred to as the unstandardized b-weights, or regression weights, are used to construct the equation.

Std.Error is the standard error associated with the B-weight.  These values indicate the expected variability of the b-weights across samples.  Smaller numbers are better.

Beta is the standardized regression coefficient and is the regression weight that would be used if the dependent and independent variables were given in z-score (standardized) form. These weights also indicate the relative importance of each variable in the equation.

t and Sig. indicate whether the individual variables make a significant contribution to the equation.  Variables that do not make significant contributions to the equation should be removed in most cases (curve fitting being the exception).  If the value of Sig is less than alpha (typically 0.05), then the variable is making a significant contribution to the model.

Zero-order, Partial, and Part correlations reflect teh simple correlations (zero-order), partial (other independent variables in the equation removed from both the listed independent variable and the dependent variable), and semi-partial correlations (other independent variables in teh equation removed from the listed independent variable).

Tolerance is the proportion of variability in the listed independent variable that is not accounted for by other independent variables in the equation.  This value indicates whether multicollinearity is present.  Tolerance should always ben greated that 0.2.