Summary of Fit for Linear Models
The Summary of Fit table for linear models, shown in
Figure 39.11, includes the following:
- Mean of Response
- is the sample mean, , of the response variable.
- Root MSE
- is the estimate of the standard deviation of the error term.
It is calculated as the square root of the mean square error.
- R2, with values between 0 and 1,
indicates the proportion of the (corrected)
total variation attributed to the fit.
- Adj R-Sq
- An adjusted R2
is a version of R2 that
has been adjusted for degrees of freedom.
Figure 39.11: Summary of Fit, Analysis of Variance Tables for Linear Models
With an intercept term in the model, R2
is defined as
R2 = 1-(SSE / CSS)
where is the corrected sum of squares and
is the sum of squares for error.
The R2 statistic is also the square of the
multiple correlation, that is, the square of the correlation
between the response variable and the predicted values.
The adjusted R2 statistic, an alternative to
R2, is adjusted for the degrees of freedom
of the sums of squares associated with R2.
It is calculated as
Adj R2 = 1-[(SSE / (n-p))/(CSS / (n-1))] = 1-[(n-1)/(n-p)] (1- R2)
Without an intercept term in the model,
R2 is defined as
where is the uncorrected total sum of squares.
R2 = 1-(SSE / TSS)
The adjusted R2 statistic is then calculated as
Adj R2 = 1-[(SSE / (n-p))/(TSS / n)] = 1-[n/(n-p)](1- R2)
|Other definitions of R2 exist for models with
no intercept term. Care should be
taken to ensure that this is the definition desired.|
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.