* ch03eg2.sas, chapter 3 example, tests involving residuals,
* using the Toluca Company data (page 19);
options ls=76;
filename data1 'toluca.dat';
;
data toluca;
 infile data1;
 input x y;
;
proc print;
;
proc reg;
 model y = x;
 output out=B p=yhat r=e;
 title 'Tests involving residuals: Toluca Company data';
;
* F-test for Lack of Fit (LOF) (Section 3.7, p119);
* The MSE generated by the ANOVA model is the MSPE;
proc glm;
 class x;
 model y = x;
* or, to get the test statistic directly...;
data B; set B;
 A=x;
proc glm;
 class A;
 model y = x A;
 * (see pp121-123 concerning full and reduced models);
 * (see p 126 for the ANOVA table, but the book uses
 *  a different example -- a Bank Example);
;                                                                
* create the normal score variable "nscore" for NP plots;        
proc rank normal=Blom; * use Blom's normal scores;               
 var e;                                                          
 ranks nscore; * nscore =  probit((rank-0.375)/(N+0.25)), see p111; 
;                                                                
* Compute sample correlation between residuals and normal        
* scores (see Section 3.5, p115);                                
proc corr nosimple; * Don't print simple statistics;             
 var e nscore;                                                   

                               The SAS System                              1

                             Obs     x      y

                               1     80    399
                               2     30    121
                               :      :      :
                              23     40    244
                              24     80    342
                              25     70    323

Reduced and full models:
----------------------------------------------------------------------------
               Tests involving residuals: Toluca Company data              2

                             The REG Procedure
                               Model: MODEL1
                           Dependent Variable: y 

                           Analysis of Variance
 
                                   Sum of          Mean
 Source                  DF       Squares        Square   F Value   Pr > F
 Model                    1        252378        252378    105.88   <.0001
 Error                   23         54825    2383.71562                   
 Corrected Total         24        307203                                 

----------------------------------------------------------------------------

               Tests involving residuals: Toluca Company data              3

                             The GLM Procedure

                          Class Level Information
 
        Class         Levels    Values

        x                 11    20 30 40 50 60 70 80 90 100 110 120 




               Tests involving residuals: Toluca Company data              4

                             The GLM Procedure
 
Dependent Variable: y   

                                     Sum of
 Source                    DF       Squares   Mean Square  F Value  Pr > F
 Model                     10   269622.2067    26962.2207    10.04  <.0001
 Error                     14    37580.8333     2684.3452                 
 Corrected Total           24   307203.0400                               


 Source                    DF     Type I SS   Mean Square  F Value  Pr > F
 x                         10   269622.2067    26962.2207    10.04  <.0001


Both models in one:
----------------------------------------------------------------------------
               Tests involving residuals: Toluca Company data              5

                             The GLM Procedure

                          Class Level Information
 
        Class         Levels    Values
        A                 11    20 30 40 50 60 70 80 90 100 110 120 


               Tests involving residuals: Toluca Company data              6

                             The GLM Procedure
 Dependent Variable: y   

                                     Sum of
 Source                    DF       Squares   Mean Square  F Value  Pr > F
 Model                     10   269622.2067    26962.2207    10.04  <.0001
 Error                     14    37580.8333     2684.3452                 
 Corrected Total           24   307203.0400                               


 Source                    DF     Type I SS   Mean Square  F Value  Pr > F
 x                          1   252377.5808   252377.5808    94.02  <.0001
 A                          9    17244.6259     1916.0695     0.71  0.6893
----------------------------------------------------------------------------

Testing normality:

               Tests involving residuals: Toluca Company data              7

                             The CORR Procedure

                      2  Variables:    e        nscore   

                 Pearson Correlation Coefficients, N = 25 
                        Prob > |r| under H0: Rho=0
 
                                              e        nscore

              e                         1.00000       0.99151
              Residual                                 <.0001

              nscore                    0.99151       1.00000
              Rank for Variable e        <.0001