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 The REG Procedure

## Model Fit and Diagnostic Statistics

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 b = (X'X)-X'Y. The subscript i denotes values for the ith observation, the parenthetical subscript (i) means that the statistic is computed 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 55.5 contains the summary statistics for assessing the fit of the model.

Table 55.5: Formulas and Definitions for Model Fit Summary Statistics
 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= option or from fitting the full model SST0 the uncorrected total sum of squares for the dependent variable SST1 the total sum of squares corrected for the mean for the dependent variable SSE the error sum of squares MSE R2 ADJRSQ AIC BIC CP (Cp) GMSEP [( MSE(n+1)(n-2))/(n(n-p-1))] = [1/n] Sp(n+1)(n-2) JP (Jp) [(n+p)/n] MSE PC [(n+p)/(n-p)] (1 - R2) = Jp ( [n/( SSTi)] ) PRESS the sum of squares of predri (see Table 55.6) RMSE SBC n ln( [ SSE/n] ) + p ln(n) SP (Sp) [ MSE/(n-p-1)]

Table 55.6 contains the diagnostic statistics and their formulas; these formulas and further information can be found in Chapter 3, "Introduction to Regression Procedures," and in the "Influence Diagnostics" section. Each statistic is computed for each observation.

Table 55.6: Formulas and Definitions for Diagnostic Statistics
 Formula PRED () Xib RES (ri) H (hi) xi(X'X)-xi' STDP STDI STDR LCL STDP LCLM STDI UCL STDP UCLM STDI STUDENT [(ri)/( STDRi)] RSTUDENT COOKD [1/p] STUDENT2([ STDP/( STDR2)]) COVRATIO DFFITS DFBETASj PRESS(predri) [(ri)/(1-hi)]

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