# Linear Regression: Saving New Variables

You can save predicted values, residuals, and other statistics useful for diagnostic information. Each selection adds one or more new variables to your active data file.

Predicted Values. Values that the regression model predicts for each case.

• Unstandardized. The value the model predicts for the dependent variable.
• Standardized. A transformation of each predicted value into its standardized form. That is, the mean predicted value is subtracted from the predicted value, and the difference is divided by the standard deviation of the predicted values. Standardized predicted values have a mean of 0 and a standard deviation of 1.
• Adjusted. The predicted value for a case when that case is excluded from the calculation of the regression coefficients.
• S.E. of mean predictions. Standard errors of the predicted values. An estimate of the standard deviation of the average value of the dependent variable for cases that have the same values of the independent variables.

Distances. Measures to identify cases with unusual combinations of values for the independent variables and cases that may have a large impact on the regression model.

• Mahalanobis. A measure of how much a case's values on the independent variables differ from the average of all cases. A large Mahalanobis distance identifies a case as having extreme values on one or more of the independent variables.
• Cook's. A measure of how much the residuals of all cases would change if a particular case were excluded from the calculation of the regression coefficients. A large Cook's D indicates that excluding a case from computation of the regression statistics changes the coefficients substantially.
• Leverage values. Measures the influence of a point on the fit of the regression. The centered leverage ranges from 0 (no influence on the fit) to (N-1)/N.

Prediction Intervals. The upper and lower bounds for both mean and individual prediction intervals.

• Mean. Lower and upper bounds (two variables) for the prediction interval of the mean predicted response.
• Individual. Lower and upper bounds (two variables) for the prediction interval of the dependent variable for a single case.
• Confidence Interval. Enter a value between 1 and 99.99 to specify the confidence level for the two Prediction Intervals. Mean or Individual must be selected before entering this value. Typical confidence interval values are 90, 95, and 99.

Residuals. The actual value of the dependent variable minus the value predicted by the regression equation.

• Unstandardized. The difference between an observed value and the value predicted by the model.
• Standardized. The residual divided by an estimate of its standard deviation. Standardized residuals, which are also known as Pearson residuals, have a mean of 0 and a standard deviation of 1.
• Studentized. The residual divided by an estimate of its standard deviation that varies from case to case, depending on the distance of each case's values on the independent variables from the means of the independent variables.
• Deleted. The residual for a case when that case is excluded from the calculation of the regression coefficients. It is the difference between the value of the dependent variable and the adjusted predicted value.
• Studentized deleted. The deleted residual for a case divided by its standard error. The difference between a Studentized deleted residual and its associated Studentized residual indicates how much difference eliminating a case makes on its own prediction.

Influence Statistics. The change in the regression coefficients (DfBeta[s]) and predicted values (DfFit) that results from the exclusion of a particular case. Standardized DfBetas and DfFit values are also available along with the covariance ratio.

• DfBeta(s). The difference in beta value is the change in the regression coefficient that results from the exclusion of a particular case. A value is computed for each term in the model, including the constant.
• Standardized DfBeta. Standardized difference in beta value. The change in the regression coefficient that results from the exclusion of a particular case. You may want to examine cases with absolute values greater than 2 divided by the square root of N, where N is the number of cases. A value is computed for each term in the model, including the constant.
• DfFit. The difference in fit value is the change in the predicted value that results from the exclusion of a particular case.
• Standardized DfFit. Standardized difference in fit value. The change in the predicted value that results from the exclusion of a particular case. You may want to examine standardized values which in absolute value exceed 2 times the square root of p/N, where p is the number of parameters in the model and N is the number of cases.
• Covariance ratio. The ratio of the determinant of the covariance matrix with a particular case excluded from the calculation of the regression coefficients to the determinant of the covariance matrix with all cases included. If the ratio is close to 1, the case does not significantly alter the covariance matrix.

Coefficient Statistics. Saves regression coefficients to a dataset or a data file. Datasets are available for subsequent use in the same session but are not saved as files unless explicitly saved prior to the end of the session. Dataset names must conform to variable naming rules. See the topic Variable names for more information.

Export model information to XML file. Parameter estimates and (optionally) their covariances are exported to the specified file in XML (PMML) format. You can use this model file to apply the model information to other data files for scoring purposes. See the topic Scoring Wizard for more information.

Saving New Variables in Linear Regression

This feature requires the Statistics Base option.