* reg.sas, for test 2, fall 97;
options ls=72;
;
data A;
 input y x;
 x2=x*x; A=x;
 lines;
 25.2 10
 27.3 10
 28.7 10
 29.8 15
 31.1 15
 27.8 15
 31.2 20
 32.6 20
 29.7 20
 31.7 25
 30.1 25
 32.3 25
 29.4 30
 30.8 30
 32.8 30
;
proc glm;
 class A;
 model y = A;
proc reg;
 model y = x x2 / ss1 ss2;
 output out=B p=yhat r=e;
proc rank normal=Blom;
 var e;
 ranks nscore;
proc plot;
 plot e*x e*yhat / vref=0 vpos=20;
 plot e*nscore / href=0 vref=0 vpos=20;
proc corr nosimple;
 var x y e nscore;

                             The SAS System                            1

                    General Linear Models Procedure
                        Class Level Information

                   Class    Levels    Values

                   A             5    10 15 20 25 30


                Number of observations in data set = 15





                             The SAS System                            2

                    General Linear Models Procedure

Dependent Variable: Y   
                                  Sum of         Mean
Source                  DF       Squares       Square  F Value    Pr > F

Model                    4     39.046667     9.761667     4.01    0.0342

Error                   10     24.366667     2.436667

Corrected Total         14     63.413333

                  R-Square          C.V.     Root MSE             Y Mean

                  0.615749      5.197500       1.5610             30.033


Source                  DF     Type I SS  Mean Square  F Value    Pr > F

A                        4     39.046667     9.761667     4.01    0.0342

Source                  DF   Type III SS  Mean Square  F Value    Pr > F

A                        4     39.046667     9.761667     4.01    0.0342



                             The SAS System                            3

Model: MODEL1  
Dependent Variable: Y                                                  

                          Analysis of Variance

                          Sum of         Mean
 Source          DF      Squares       Square      F Value       Prob>F

 Model            2     38.93714     19.46857        9.545       0.0033
 Error           12     24.47619      2.03968
 C Total         14     63.41333

     Root MSE       1.42817     R-square       0.6140
     Dep Mean      30.03333     Adj R-sq       0.5497
     C.V.           4.75530

                          Parameter Estimates

                   Parameter      Standard    T for H0:               
  Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

  INTERCEP   1     19.033333    3.27754909         5.807        0.0001
  X          1      1.008571    0.35643104         2.830        0.0152
  X2         1     -0.020381    0.00881488        -2.312        0.0393

                                          
  Variable  DF     Type I SS    Type II SS

  INTERCEP   1         13530     68.785021
  X          1     28.033333     16.331455
  X2         1     10.903810     10.903810

                             The SAS System                            4

            Plot of E*X.  Legend: A = 1 obs, B = 2 obs, etc.

         |
       2 +
         |                                                      A
         |  A            A            A
         |
         |
    R    |                                         A
    e    |
    s    |
    i    |  A            A            A            A
    d  0 +---------------------------------------------------------
    u    |                                                      A
    a    |
    l    |
         |
         |
         |                            A            A
         |                                                      A
         |  A            A
      -2 +
         ---+------------+------------+------------+------------+--
           10           15           20           25           30

                                      X

                                                                        
                             The SAS System                            5

          Plot of E*YHAT.  Legend: A = 1 obs, B = 2 obs, etc.

     |
   2 +
     |                                                   A
     | A                               A                   A
     |
     |
R    |                                                           A
e    |
s    |
i    | A                               A                   A     A
d  0 +------------------------------------------------------------------
u    |                                                   A
a    |
l    |
     |
     |
     |                                                     A     A
     |                                                   A
     | A                               A
  -2 +
     -+------------+------------+------------+------------+------------+
     27           28           29           30           31           32

                             Predicted Value of Y
                                                                        
                             The SAS System                            6

         Plot of E*NSCORE.  Legend: A = 1 obs, B = 2 obs, etc.

         |                            |
       2 +                            |
         |                            |                      A
         |                            |        A  A   A
         |                            |
         |                            |
    R    |                            |      A
    e    |                            |
    s    |                            |
    i    |                          A A A A
    d  0 +----------------------------+----------------------------
    u    |                        A   |
    a    |                            |
    l    |                            |
         |                            |
         |                            |
         |                   A A      |
         |                A           |
         |     A      A               |
      -2 +                            |
         ---+------------+------------+------------+------------+--
           -2           -1            0            1            2

                             RANK FOR VARIABLE E


                                                                        
                             The SAS System                            7

                          Correlation Analysis

          4 'VAR' Variables:  X        Y        E        NSCORE  


Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 15  

                               X            Y            E       NSCORE

X                        1.00000      0.66489      0.00000      0.08040
                          0.0          0.0068       1.0000       0.7758

Y                        0.66489      1.00000      0.62127      0.64805
                          0.0068       0.0          0.0134       0.0090

E                        0.00000      0.62127      1.00000      0.96060
Residual                  1.0000       0.0134       0.0          0.0001

NSCORE                   0.08040      0.64805      0.96060      1.00000
RANK FOR VARIABLE E       0.7758       0.0090       0.0001       0.0