# Multiple Regression Analysis - Advanced Tab

Principal Components and Factor Analysis

Select the Advanced tab of the Multiple Regression Analysis dialog box to access options that offer a greater variety of multiple regression techniques than those available on the Quick tab.

Variables. Click the Variables button to display a standard variable selection dialog box, in which you select the dependent variable and the independent variables. After you have selected variables, The Multiple regression results field displays the R, R2, adjusted R2, F and p statistics.

Tolerance. Specify the minimum tolerance that is considered acceptable by STATISTICA in the Tolerance box. The minimum value that can be specified here is 1.00E-25 (i.e., a number with 24 zeros past the decimal point). However, it is not recommended to enter such an extremely low value. If the tolerance of a variable entered into the regression equation is less than the default tolerance value (.01) it means that this variable is 99 percent redundant with (identical to) the variables already in the equation. Forcing very redundant variables into the regression equation is not only questionable in terms of relevance of results, but the resultant estimates (regression coefficients) will become increasingly unreliable.

The tolerance of a variable is defined as 1 minus the squared multiple correlation of this variable with all other independent variables in the regression equation. Therefore, the smaller the tolerance of a variable, the more redundant is its contribution to the regression (i.e., it is redundant with the contribution of other independent variables). If the tolerance of any of the variables in the regression equation is equal to zero (or very close to zero) then the regression equation cannot be evaluated (the matrix is said to be ill-conditioned, and it cannot be inverted, see Note).

Summary: Regression coefficients. Click the Summary: Regression coefficients button to produce a spreadsheet with the standardized (beta) and nonstandardized (B) regression coefficients (weights), their standard error, and statistical significance. The summary statistics for the regression analysis (e.g., R, R-square, etc.) are displayed in the header of the spreadsheet.

Partial corrs. Click the Partial corrs button to display spreadsheets with:

1. The beta in (standard regression coefficient for the respective variable if it were to enter into the regression equation as an independent variable);

2. The partial correlation (between the respective variable and the dependent variable, after controlling for all other independent variables in the equation);

3. The semi-partial (part) correlation (the correlation between the unadjusted dependent variable with the respective variable after controlling for all independent variables in the equation);

4. The tolerance for the respective variable (defined as 1 minus the squared multiple correlation between the respective variable and all independent variables in the regression equation);

5. The minimum tolerance (the smallest tolerance among all independent variables in the equation if the respective variable were to be entered as an additional independent variable);

6. The t-value associated with these statistics for the respective variable;

7. The statistical significance of the t-value.

These statistics will first be displayed separately for variables not currently in the regression equation (if any), and for the variables in the regression equation.

Save pred./resid. Click the Save pred./resid button to save the predicted and residual values for the current regression equation. This button is only available if a raw data file is analyzed (not a matrix file).

Alpha level for highlighting. Specify the desired Alpha level (.0001 < a < .5) in the Alpha level for highlighting box. This value is used for highlighting significant results in the spreadsheet. The default value for Alpha is .05. The value is used to determine the significance of a specific effect. If the p-value is less than or equal to the designated value for Alpha, we say that the effect is significant and it is highlighted in the spreadsheet.