* f97t1q1.sas;
* STT 646, test 1, question 1;
;
options ls=72;
data calls;
 input callno x y;
 A=x;
 lines;
   1 4 109
   2 2  58
   3 5 138
   4 7 189
   5 1  37
   6 3  82
   7 4 103
   8 5 134
   9 2  68
  10 4 112
  11 6 154
;
proc print;
 title 'STT 646, test 1, question 1.';
;
proc plot; 
 plot y*x / vpos=25;
;
proc reg;
 model y = x;
 output out=B p=yhat r=e;
 title2 'Simple linear regression.';
;
proc rank normal=Blom;
 var e;
 ranks nscore;
;
proc print;
;
proc plot;
 plot e*x e*callno e*yhat e*nscore / vpos=20 vref=0;
;
proc glm; class x;
 model y = x;
;
proc corr nosimple; 
 var e nscore;
;
proc sort; by x;
proc means noprint n var; by x;
 var y;
 output out=means n=n var=s2;
proc print; var x n s2;

                      STT 646, test 1, question 1.                     1
                                        11:47 Wednesday, October 8, 1997

                     OBS    CALLNO    X     Y     A
                       1       1      4    109    4
                       2       2      2     58    2
                       3       3      5    138    5
                       4       4      7    189    7
                       5       5      1     37    1
                       6       6      3     82    3
                       7       7      4    103    4
                       8       8      5    134    5
                       9       9      2     68    2
                      10      10      4    112    4
                      11      11      6    154    6



                      STT 646, test 1, question 1.                     2
                                        11:47 Wednesday, October 8, 1997

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

200 +
    |                                                                  A
    |
    |
    |
    |
150 +                                                       A
    |                                            A
    |                                            A
  Y |
    |
    |                                 B
100 +                                 A
    |
    |                      A
    |
    |           A
    |           A
 50 +
    |
    |A
    |
    |
    |
  0 +
    -+----------+----------+----------+----------+----------+----------+
     1          2          3          4          5          6          7

                                      X                                                                        
                      STT 646, test 1, question 1.                     3
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

Model: MODEL1  
Dependent Variable: Y                                                  

                          Analysis of Variance

                          Sum of         Mean
 Source          DF      Squares       Square      F Value       Prob>F
 Model            1  19918.84380  19918.84380      935.149       0.0001
 Error            9    191.70166     21.30018
 C Total         10  20110.54545

     Root MSE       4.61521     R-square       0.9905
     Dep Mean     107.63636     Adj R-sq       0.9894
     C.V.           4.28778

                          Parameter Estimates

                   Parameter      Standard    T for H0:               
  Variable  DF      Estimate         Error   Parameter=0    Prob > |T|
  INTERCEP   1     11.464088    3.43902571         3.334        0.0087
  X          1     24.602210    0.80451424        30.580        0.0001




                      STT 646, test 1, question 1.                     4
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

   OBS    CALLNO    X     Y     A      YHAT         E        NSCORE
     1       1      4    109    4    109.873    -0.87293    -0.22469
     2       2      2     58    2     60.669    -2.66851    -0.46149
     3       3      5    138    5    134.475     3.52486     0.72791
     4       4      7    189    7    183.680     5.32044     1.06056
     5       5      1     37    1     36.066     0.93370     0.22469
     6       6      3     82    3     85.271    -3.27072    -0.72791
     7       7      4    103    4    109.873    -6.87293    -1.59322
     8       8      5    134    5    134.475    -0.47514     0.00000
     9       9      2     68    2     60.669     7.33149     1.59322
    10      10      4    112    4    109.873     2.12707     0.46149
    11      11      6    154    6    159.077    -5.07735    -1.06056
                      STT 646, test 1, question 1.                     5
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

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

      |
      |
   10 +
      |
      |            A
      |
R   5 +                                                              A
e     |                                          A
s     |                                A
i     |  A
d   0 +------------------------------------------A----------------------
u     |                                A
a     |            A
l     |                      A
   -5 +                                                    A
      |                                A
      |
      |
  -10 +
      |
      ---+---------+---------+---------+---------+---------+---------+--
         1         2         3         4         5         6         7

                                       X

                                                                        
                      STT 646, test 1, question 1.                     6
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

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

      |
      |
   10 +
      |
      |                                                  A
      |
R   5 +                    A
e     |              A
s     |                                                        A
i     |                          A
d   0 +--------------------------------------------A--------------------
u     |  A
a     |        A
l     |                                A
   -5 +                                                              A
      |                                      A
      |
      |
  -10 +
      |
      ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--
         1     2     3     4     5     6     7     8     9    10    11

                                    CALLNO

                                                                        
                      STT 646, test 1, question 1.                     7
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

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

      |
      |
   10 +
      |
      |            A
      |
R   5 +                                                              A
e     |                                          A
s     |                                A
i     |  A
d   0 +------------------------------------------A----------------------
u     |                                A
a     |            A
l     |                      A
   -5 +                                                    A
      |                                A
      |
      |
  -10 +
      |
      ---+---------+---------+---------+---------+---------+---------+--
       36.07     60.67     85.27    109.87    134.48    159.08    183.68

                             Predicted Value of Y

                                                                        
                      STT 646, test 1, question 1.                     8
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

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

          |
          |
       10 +
          |
          |                                                 A
          |
    R   5 +                                          A
    e     |                                     A
    s     |                                  A
    i     |                               A
    d   0 +----------------------------A----------------------------
    u     |                         A
    a     |                      A
    l     |                   A
       -5 +              A
          |       A
          |
          |
      -10 +
          |
          ---+------------+------------+------------+------------+--
            -2           -1            0            1            2

                              RANK FOR VARIABLE E

                                                                        
                      STT 646, test 1, question 1.                     9
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

                    General Linear Models Procedure
                        Class Level Information

                    Class    Levels    Values
                    X             7    1 2 3 4 5 6 7

                Number of observations in data set = 11



                      STT 646, test 1, question 1.                    10
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

                    General Linear Models Procedure

Dependent Variable: Y   
                                  Sum of         Mean
Source                  DF       Squares       Square  F Value    Pr > F
Model                    6     20010.545     3335.091   133.40    0.0001
Error                    4       100.000       25.000
Corrected Total         10     20110.545

                  R-Square          C.V.     Root MSE             Y Mean
                  0.995027      4.645270       5.0000             107.64

Source                  DF     Type I SS  Mean Square  F Value    Pr > F
X                        6     20010.545     3335.091   133.40    0.0001

Source                  DF   Type III SS  Mean Square  F Value    Pr > F
X                        6     20010.545     3335.091   133.40    0.0001



                      STT 646, test 1, question 1.                    11
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

                          Correlation Analysis

                   2 'VAR' Variables:  E        NSCORE  


Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 11  

                                            E            NSCORE

        E                             1.00000           0.99730
        Residual                       0.0               0.0001

        NSCORE                        0.99730           1.00000
        RANK FOR VARIABLE E            0.0001            0.0   






                      STT 646, test 1, question 1.                    12
                       Simple linear regression.
                                        11:47 Wednesday, October 8, 1997

                          OBS    X    N    S2
                           1     1    1     .
                           2     2    2    50
                           3     3    1     .
                           4     4    3    21
                           5     5    2     8
                           6     6    1     .
                           7     7    1     .