Multiple Regression - Computational Approach

Click the OK button in the Model Definition dialog box to display the Multiple Regression Results dialog box, which contains three tabs: Quick, Advanced, and Residuals/assumptions/prediction. These tabs show the summary of results for the current regression analysis and offers several options to review specific results. Note that this dialog box is also displayed when you click OK in the Multiple Linear Regression Startup Panel and the Review Descriptive Statistics dialog box.

Summary Box. The Summary box at the top of the dialog box summarizes the following information:

Dependent. The Dependent. field contains the name of the dependent variable.

Multiple R. The Multiple R field contains the coefficient of multiple correlation, which is the positive square root of R-square (the coefficient of multiple determination, see Residual variance and R-square). This statistic is useful in multivariate regression (i.e., multiple independent variables) when you want to describe the relationship between the variables.

F, df, and p-value. The F-value, df, and resulting p-value is used as an overall F-test of the relationship between the dependent variable and the set in independent variables. Here:

F = Regression Mean Square/Residual Mean Square.

R2. The R2 (R-square) field contains the coefficient of multiple determination, which measures the reduction in the total variation of the dependent variable due to the (multiple) independent variables.

R-square = 1 - [Residual SS/Total SS]

Residual SS is the error sums of squares and the Total SS is the total sums of squares.

No. of cases. The No. of cases field contains the minimum valid sample size (N) depending on the MD Deletion option that you selected.

Adjusted R2. The Adjusted R2 is interpreted similarly to the R2 value except the adjusted R2 takes into consideration the number of degrees of freedom. It is adjusted by dividing the error sum of squares and total sums of square by their respective degrees of freedom.

R-square (adjusted) = 1 - [(Residual SS/df)/(Total SS/df)]

Standard error of estimate. The Standard error of estimate measures the dispersion of the observed values about the regression line.

Intercept. The Intercept field contains the intercept value if you selected to include the intercept in the model on the Model Definition - Advanced tab.

Std. Error. The Std. error field contains the standard error of the intercept.

t(df) and p-value. The t-value and resulting p-value are used to test the hypothesis that the intercept is equal to 0.

Model Box. Statistically significant regression coefficients (Beta coefficients) for the variables in the analysis are highlighted in this box. The criterion for determining statistical significance (alpha level) can be changed from the .05 default in the Alpha for highlighting effects field.

Copy button. Click the Copy button to copy either the selected text (if text has been selected) in the Summary box or Model box or all of the text (if no text has been selected) to the Clipboard. Note that the copied text retains formatting information (such as font, color, etc.).

Contract/Expand button. Click the Contract/Expand button to contract or expand the Summary box and Model box. When contracted, you can see only one line of the Summary box or Model box text and can scroll through the text using a scroll bar. Note that when contracted the text is scrolled so that the first non-blank line is at the top. When expanded (the default setting), the entire Summary box and Model box will be displayed on the Multiple Regression Results dialog.

Alpha for highlighting effects. Adjust the Alpha for highlighting effects by entering a new value in the edit box or using the microscroll buttons. The default value is .05. For more details on p-value, see Elementary Concepts.

OK. Click the OK button to display the Residual Analysis dialog box.

Cancel. Click the Cancel button to close the dialog box and return to the Multiple Linear Regression Startup Panel or the Model Definition dialog box.

Options. Click the Options button to display the Options menu.

By Group. Click the By Group button to display the By Group specification dialog box.