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 i^{th} case in the
model. These residuals have t  distributions with ( nk1) 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 i^{th} observation
omitted, using the model to predict the i ^{th} observation and then
computing the difference from the actual i^{th} 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 i^{th}
datapoint on the estimated regression coefficient. In linear models Cook's
Distance has, approximately, an F distribution with k and (nk) 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 i^{th} 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 i^{th}
observation.
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 pvalue for the Ftest is zero. This means the overall regression is significant.
