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Residuals (Multiple Linear Regression...)

Residuals option of regression can be used to compute various types of residuals and influence statistics for the regression analysis.

To learn more about Residuals option of regression click on ....



About the Residuals dialog box



Anova Table
When this checkbox is checked the ANOVA table is displayed in the output.

Fitted values
When this checkbox is checked the fitted values are displayed in the output. .

Unstandardized
When this checkbox is checked the Unstandardized Residuals are displayed in the output. Unstandardized residuals are computed by the formula
Unstandardized residual = Actual response - Predicted response

Standardized
When this checkbox is checked the Standardized Residuals are displayed in the output. Standardised residuals are obtained by dividing the unstandardized residuals by respective standard deviations.

Studentised
When this checkbox is checked the Studentised Residuals are displayed in the output. Studentised residuals are computed by dividing the unstandardized residuals by quantities related to the diagonal elements of the hat matrix , using a common scale estimate computed without the ith case in the model. These residuals have t - distributions with ( n-k-1) degrees of freedom, so any residual with absolute values exceeding 3 usually require attention.

Deleted
When this checkbox is checked the Deleted Residuals are displayed in the output. These are obtained by fitting the model with ith observation omitted, using the model to predict the i th observation and then computing the difference from the actual ith observation.

Cook's Distance
When this checkbox is checked the Cook's Distance for each observation is displayed in the output. This is an overall measure of the impact of the ith datapoint on the estimated regression coefficient. In linear models Cook's Distance has, approximately, an F distribution with k and (n-k) degrees of freedom.

DFFIT's
When this checkbox is checked the DFFIT's (change in the regression fit) for each observation is displayed in the output. These reflect coefficient changes as well as forecasting effects when an observation is deleted.

Covariance Ratios
When this checkbox is checked the Covariance Ratios are displayed in the output. This measure reflects the change in the variance -covariance matrix of the estimated coefficients when the ith observation is deleted.

Hat matrix Diagonal
When this checkbox is checked the Diagonal elements of the hat matrix are displayed in the output. This measure is also known as leverage of the ith observation.

Example

Following outputs are produced when the options shown above in Residuals dialog image are selected. This output is produced along with the Default output for the same input data. When we study the ANOVA table we find that p-value for the F-test is zero. This means the overall regression is significant.

 


StatCalc also produces various residuals and influence statistics. These are produced for each observation. Here we have displayed the statistics only for the first ten observations. These can be studied to find out outliers and influencial observations.