# Linear Regression Statistics

The following statistics are available:

**Regression Coefficients -**
Estimates displays Regression coefficient *B*, standard error of
*B*, standardized coefficient beta, *t* value for *B*, and two-tailed significance
level of *t*. Confidence intervals displays confidence intervals with
the specified level of confidence for each regression coefficient or a covariance matrix.
Covariance matrix displays a variance-covariance matrix of regression
coefficients with covariances off the diagonal and variances on the diagonal. A correlation matrix
is also displayed.

**Model fit -** The variables that are entered and removed from the model are listed, and the
following 'goodness-of-fit statistics' are displayed: multiple *R*, *R*
^{2} and adjusted *R*
^{2}, standard error of the estimate, and an analysis-of-variance table.

**R squared change - **The change in the *R*
^{2} statistic that is produced by adding or deleting an independent variable. If the
*R*
^{2} change associated with a variable is large, that means that the variable is a good
predictor of the dependent variable.

**Descriptive -** Provides the number of valid cases, the mean, and the standard deviation for
each variable in the analysis. A correlation matrix with a one-tailed significance level and the
number of cases for each correlation are also displayed.

Part Correlation. The correlation between the dependent variable and an independent variable when the linear effects of the other independent variables in the model have been removed from the independent variable. It is related to the change in R-squared when a variable is added to an equation. Sometimes called the semipartial correlation.

Partial Correlation. The correlation that remains between two variables after removing the correlation that is due to their mutual association with the other variables. The correlation between the dependent variable and an independent variable when the linear effects of the other independent variables in the model have been removed from both.

**Collinearity diagnostics -** Collinearity (or multicollinearity) is the undesirable situation
when one independent variable is a linear function of other independent variables. Eigenvalues of
the scaled and uncentered cross-products matrix, condition indices, and variance-decomposition
proportions are displayed along with variance inflation factors (VIF) and tolerances for individual
variables.

**Selection criteria -** Includes Akaike information criterion (AIC), Ameniya’s prediction
criterion (PC), Mallows conditional mean squared error of prediction criterion (Cp), and Schwarz
Bayesian criterion (SBC). The statistics are displayed in the Model Summary table.

**Residuals - **You can select **'PRESS Statistic'** to use as a cross-validation statistic to
compare different models. This also displays the **'Durban-Watson'** test for serial correlation
of the residuals. Choose the **'Case wise diagnostic'** information for the cases that meet the
selection criterion (outliers above *n* standard deviations).

Requesting Statistics with a Regression

This feature requires the Statistics Base option.

- From the
menus choose:
- In the Linear Regression dialog box, click Statistics.
- Select the statistics that you want.