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.
 RSquare
 R^{2}, with values between 0 and 1,
indicates the proportion of the (corrected)
total variation attributed to the fit.
 Adj RSq
 An adjusted R^{2}
is a version of R^{2} 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, R^{2}
is defined as

R^{2} = 1(SSE / CSS)
where is the corrected sum of squares and
is the sum of squares for error.
The R^{2} 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 R^{2} statistic, an alternative to
R^{2}, is adjusted for the degrees of freedom
of the sums of squares associated with R^{2}.
It is calculated as

Adj R^{2} = 1[(SSE / (np))/(CSS / (n1))] = 1[(n1)/(np)] (1 R^{2})
Without an intercept term in the model,
R^{2} is defined as

R^{2} = 1(SSE / TSS)
where is the uncorrected total sum of squares.
The adjusted R^{2} statistic is then calculated as

Adj R^{2} = 1[(SSE / (np))/(TSS / n)] = 1[n/(np)](1 R^{2})
Note  Other definitions of R^{2} 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.