* test1q2.sas;
* STT 646, test 1, question 1;
;
options ls=72;
;
data A;
 input x y;
 lines;
      10    39.1
      10    26.9
      10    37.9
      10    37.9
      20    63.5
      20    41.6
      20    74.3
      20    65.1
      30    49.8
      30    85.2
      30   137.6
      30    98.3
      40   191.4
      40   109.4
      40    92.9
      40    91.4
;
proc print;
 title 'STT 646, test 1, question 2.';
;
proc plot;
 plot y*x / vpos=20;
 title2 'Plot of the raw data.';
;
proc reg;
 model y = x;
 output out=B p=yhat r=e;
;
proc plot; 
 plot e*yhat / vpos=20;
;
proc sort; by x;
proc means noprint; by x;
 var y;
 output out=C mean=xbar var=s2;
proc print;
 var x xbar s2;
;
;
;
;
;
data C; set C;
 ln_xbar = log(xbar);
 ln_s2 = log(s2);
proc plot;
 plot ln_s2*ln_xbar / vpos=20;


                      STT 646, test 1, question 2.                     1
                                        14:45 Wednesday, October 8, 1997

                           OBS     X      Y

                             1    10     39.1
                             2    10     26.9
                             3    10     37.9
                             4    10     37.9
                             5    20     63.5
                             6    20     41.6
                             7    20     74.3
                             8    20     65.1
                             9    30     49.8
                            10    30     85.2
                            11    30    137.6
                            12    30     98.3
                            13    40    191.4
                            14    40    109.4
                            15    40     92.9
                            16    40     91.4
                      STT 646, test 1, question 2.                     2
                         Plot of the raw data.
                                        14:45 Wednesday, October 8, 1997

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

       Y |
     200 +
         |                                                     A
         |
         |
         |
         |
         |                                    A
         |
         |                                                     A
     100 +                                    A
         |                                    A                B
         |                   A
         |                   B
         |
         |  A                A                A
         |  B
         |  A
         |
       0 +
         ---+----------------+----------------+----------------+--
           10               20               30               40

                                     X

                                                                        
                      STT 646, test 1, question 2.                     3
                         Plot of the raw data.
                                        14:45 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  16712.87112  16712.87112       20.526       0.0005
 Error           14  11399.26825    814.23345
 C Total         15  28112.13937

     Root MSE      28.53478     R-square       0.5945
     Dep Mean      77.64375     Adj R-sq       0.5655
     C.V.          36.75090

                          Parameter Estimates

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

  INTERCEP   1      5.375000   17.47391034         0.308        0.7629
  X          1      2.890750    0.63805699         4.531        0.0005

                      STT 646, test 1, question 2.                     4
                         Plot of the raw data.
                                        14:45 Wednesday, October 8, 1997

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

            |
        100 +
            |
            |
            |
            |                                                  A
      R     |
      e  50 +
      s     |                                  A
      i     |
      d     |
      u     |
      a     |  A               A               A
      l   0 +  B               B
            |  A                               A               A
            |
            |                  A                               A
            |                                                  A
            |                                  A
        -50 +
            ---+---------------+---------------+---------------+--
             34.28           63.19           92.10          121.01

                             Predicted Value of Y

                                                                        
                      STT 646, test 1, question 2.                     5
                         Plot of the raw data.
                                        14:45 Wednesday, October 8, 1997

                    OBS     X      XBAR        S2

                     1     10     35.450      32.81
                     2     20     61.125     192.08
                     3     30     92.725    1314.68
                     4     40    121.275    2252.06
                      STT 646, test 1, question 2.                     6
                         Plot of the raw data.
                                        14:45 Wednesday, October 8, 1997

       Plot of LN_S2*LN_XBAR.  Legend: A = 1 obs, B = 2 obs, etc.

LN_S2 |
    8 +
      |                                                      A
      |                                           A
      |
      |
      |
    6 +
      |
      |                           A
      |
      |
      |
    4 +
      |
      |     A
      |
      |
      |
    2 +
      ---+---------+---------+---------+---------+---------+---------+--
       3.50      3.75      4.00      4.25      4.50      4.75      5.00

                                    LN_XBAR