Multiple Regressions

Selecting (Designs, Regression Models, Multiple Regression Analysis - Two Predictor Variables) and clicking the Accept command, variables X1, X2 and Y will be imposed on the vector display. Clicking on the Analysis I menu, selecting Multiple Regression Analysis, marking Predictor Variables X1 and X2 and the Criterion Variable Y,

and clicking the Accept command, variables B1, B2, Y' and Y^ will be added to the display. Click on Descriptive Statistics and select the Standardize Variance command. When asked to Select the Standardizing Variable, select the criterion variable Y and click the Accept command.

Notice that standard variances of variables Y' and Y^ sum to 1.00, but the standard variances of B1 (.102) and B2 (.365) do not sum to the standard variance of Y' (.582).

Estimation Phase of the Multiple Regression Analysis

Unfold the output panel of the Multiple Regression Analysis

and click the Information command

Delete the criterion variable Y and the results of the multiple regression analysis from the vector display (Data, Delete Variables)

and click the Clear Selected Variable(s) command. Right click the Descriptive Statistics command to remove the standard variance from descriptive statistics on the bottom of the vector display. Select (Project, Project Name) and name this new project "Estimation Phase of the Multiple Regression Analysis."

For this hypothetical example, assume that the predictor variables X1 and X2 contain new values, obtained from another set of subjects. Also, notice that the Scalar module contains the obtained regression weights B Weight 1, B Weight 2, and the Intercept A.

Select (Operations, Multiply by a Constant). Mark the Predictor Variable X1, Name the Product B1, drag the Constant B Weight 1 from the Scalar module, and click the Append command.

Repeat this for the Predictor Variable X2. Select (Operations, Add Variables), add B1 and B2, and Name the Sum Y'. Select (Operations, Add a Constant), drag the Intercept A form the Scalar module to the Constant input box, select variable Y', Name the Sum Y', and click the Replace command.

For this hypothetical example, the predicted variable Y' is identical for both the development and estimation phases of the Multiple Regression Analysis. You may also add the +-1, +-2, or +-3 sigma confidence intervals (Operations, Subtract a Constant) and (Operations, Add a Constant) as

for the +- 1 sigma confidence interval.

Multiple Regressions with Orthogonal Predictor Variables Select (Designs, Orthogonal Designs, Multiple Regression Analysis with Three Orthogonal Predictor Variables), and make sure that variables O1, O2, and O3 are not correlated (Analysis I, Correlation Matrices), i.e.,

Click the Analysis I menu, select Multiple Regression Analysis, and variables B1, B2, Y' and Y^ will be added to the display. Click on Descriptive Statistics and select the Standardize Variance command. When asked to Select the Standardizing Variable, select the criterion variable Y and click the Accept command. At this point the vector display will look as

Open and clear the Scalar module and transfer the standard variance for variables B1, B2, B3, Y' and Y^ to the Scalar module, as

Note that in the case of the orthogonal predictor variables not only the standard variances of variables Y' (.835) and Y^ (.165) add to 1.00, but also the standard variances of B1 (.812), B2 (.005), and B3 (.018) do sum to the standard variance of Y' (.835).