Multiple Regression - Computational Approach

Select the Residuals/assumptions/prediction tab of the Multiple Regression Results dialog box to access options to perform residual analysis. Additional results are available on the remaining two tabs: Quick and Advanced.

Perform residual analysis. Click the Perform residual analysis button to display the Residual Analysis dialog box. From these options you can choose to review statistics and graphs in order to perform residual analysis. Note that Perform residual analysis button may not be available if you choose Correlation Matrix as your Input file on the Multiple Linear Regression Startup Panel - Advanced tab.

Descriptive statistics. Click the Descriptive statistics button to display the Review Descriptive Statistics dialog box. Use these options to review the means and standard deviations, the correlation matrix and the covariance matrix, or choose to display the correlation matrix in a standard matrix spreadsheet.

Code generator. If your program is licensed to include this feature, you can generate computer code to implement the current model for predicting new observations. When you click this button you have the following choices:

STATISTICA Visual Basic (SVB). Select this option to generate a STATISTICA Visual Basic program containing the code implementing the model. This code will be generated in a form compatible with the nodes of STATISTICA Data Miner; however, you can also simply copy/paste the relevant portion of this code to include it in your custom Visual Basic programs. The code will automatically be displayed in the STATISTICA Visual Basic program editor window.

C/C++ language. Select this option to generate code compatible with the C/C++ computer language. This option is useful if you want to include the information provided by the final model into custom (C/C++) programs. (See also, Using C/C++/C# Code for Deployment.)

PMML script. This command will generate code in Predictive Model Markup Language (PMML), which is an XML-based language for storing information about fully trained (parameterized) models, and for sharing those models with other applications. STATISTICA and STATISTICA Enterprise Server contain facilities to use this information to compute predicted values or classifications, i.e., to quickly and efficiently deploy models (typically in the context of data mining projects).

Deployment to STATISTICA Enterprise. Select this command to deploy the results as an Analysis Configuration in STATISTICA Enterprise. Note that appropriately formatted data must be available in a STATISTICA Enterprise Data Configuration before the results can be deployed to an Analysis Configuration.

Predict values. The options in the Predict values group box are used to make predictions for the dependent variable using the specified model.

Predict dependent variable. Click the Predict dependent variable button to display the Specify Values for Indep. Vars dialog box, which is used to enter values for each independent variable in the regression equation and to calculate the predicted value for the dependent variable based on the current regression equation. The predicted value will then be displayed in the Predicting Values spreadsheet.

Compute confidence limits. Select the Compute confidence limits option button to display the confidence limits (labeled CL) for the predicted value in the Predicting Values spreadsheet.

Note: computing the confidence limits. The 1-Alpha confidence limits for a given value(s) of X is calculated as

Y-hath ± t(1-α/2,n-p)s(Y-hath)

where n = number of cases and p = number of parameters in the model

where

s2 (Y-hath) = MSE(Xh'(X'X)-1Xh )

Compute prediction limits. Select the Compute prediction limits option button to display the prediction limits (labeled PL) for the predicted value in the Predicting Values spreadsheet.

Note: computing the Prediction limits. The 1-Alpha prediction interval for a given value(s) of X is calculated as

Y-hath ± t(1-α/2,n-p)s(Yh(new))

where

s2(Yh(new)) = [ MSE + s2 (Y-hath) = MSE + X' hs2(b)Xh]

= MSE (1 + Xh'(X'X)-1Xh)

Alpha. Enter the respective Alpha value for the confidence or prediction limits in the Alpha field. STATISTICA will compute the 1-Alpha confidence limits for the expected value (mean) of the dependent variable, or the 1-Alpha prediction limits for individual predictions of the dependent variable (see also Neter, Wasserman, & Kutner, 1985, for details).