# 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 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.

**Descriptives.** 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.

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.

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.

**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.

**Residuals. **Displays the Durbin-Watson test for serial correlation
of the residuals and casewise diagnostic information for the cases
meeting 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 you want.