This section gathers the formulas for the statistics available in the MODEL , PLOT , and OUTPUT statements. The model to be fit is , and the parameter estimate is denoted by . The subscript i denotes values for the ith observation, the parenthetical subscript means that the statistic is computed by using all observations except the ith observation, and the subscript jj indicates the jth diagonal matrix entry. The ALPHA= option in the PROC REG or MODEL statement is used to set the value for the t statistics.
Table 85.7 contains the summary statistics for assessing the fit of the model.
Table 85.7: Formulas and Definitions for Model Fit Summary Statistics
Model Option or Statistic 
Definition or Formula 

n 
the number of observations 
p 
the number of parameters including the intercept 
i 
1 if there is an intercept, 0 otherwise 

the estimate of pure error variance from the SIGMA= 

the uncorrected total sum of squares for the dependent 

the total sum of squares corrected for the mean for the 

the error sum of squares 



















the sum of squares of (see Table 85.8) 






Table 85.8 contains the diagnostic statistics and their formulas; these formulas and further information can be found in Chapter 4: Introduction to Regression Procedures, and in the section Influence Statistics. Each statistic is computed for each observation.
Table 85.8: Formulas and Definitions for Diagnostic Statistics
MODEL Option or Statistic 
Formula 

PRED () 

RES () 

H () 

STDP 

STDI 

STDR 

LCL 
STDI 
LCLM 
STDP 
UCL 
STDI 
UCLM 
STDP 
STUDENT 

RSTUDENT 

COOKD 

COVRATIO 

DFFITS 

DFBETAS 

PRESS() 
