MTB > read 'a:\ed257\marks.dat' c1-c4
      17 ROWS READ
 
  ROW     C1    C2    C3     C4
 
    1     92    50    18     73
    2    131    46    50    115
    3    193    63    85    146
    4    132    58    43    103
   .  .  .
Recreate c4 c3 dot c1 partial regression slope ---  
 MTB > regress c4 1 c1;
 SUBC> residuals c10.   NWK  p.387 (11.1b) e(Y|c1)
 
 The regression equation is
 C4 = 22.7 + 0.609 C1
 
 Predictor       Coef       Stdev    t-ratio        p
 Constant       22.75       15.34       1.48    0.159
 C1           0.60931     0.09586       6.36    0.000
 
 s = 11.11       R-sq = 72.9%     R-sq(adj) = 71.1%
 
 MTB > regress c3 1 c1;
 SUBC> residuals c11.      NWK p. 387 (11.2b) e(c3|c1)
 
 The regression equation is
 C3 = - 18.8 + 0.480 C1
 
 Predictor       Coef       Stdev    t-ratio        p
 Constant      -18.76       16.48      -1.14    0.273
 C1            0.4804      0.1029       4.67    0.000
 
 s = 11.94       R-sq = 59.2%     R-sq(adj) = 56.5%
 
Use the residuals to get the partial regression slope
---see NWK Fig 11.1 p388 
 MTB > regress c10 1 c11
 
 The regression equation is
 C10 = - 0.00 + 0.208 C11
 
 Predictor       Coef       Stdev    t-ratio        p
 Constant      -0.000       2.627      -0.00    1.000
 C11           0.2083      0.2343       0.89    0.388
               ******** matches multiple regression!
 
 s = 10.83       R-sq = 5.0%      R-sq(adj) = 0.0%

PARTIAL REGRESSION PLOT  NWK Figs 11.1-11.3
 MTB > plot c10 c11

C10-                             *     *
   -                                                   *
   -                                       *
 10+                       *
   -
   -                                            *
   -
   -                                     *
  0+                  *            *     *
   -
   -                                      *
   -                          *
   -
-10+
   -                               2 *                   *
   -      *
   -
     --+---------+---------+---------+---------+---------+----C11
     -30       -20       -10         0        10        20
 

Repeat to get partial regression slope for  c4 c1 dot c3
 MTB > regress c1 1 c3;
 SUBC> residuals c20.
 
 The regression equation is
 C1 = 87.4 + 1.23 C3
 
 Predictor       Coef       Stdev    t-ratio        p
 Constant       87.40       15.74       5.55    0.000
 C3            1.2326      0.2641       4.67    0.000
 
 s = 19.12       R-sq = 59.2%     R-sq(adj) = 56.5%

 MTB > regress c4 1 c3;
 SUBC> residuals c21.
 
 The regression equation is
 C4 = 71.2 + 0.836 C3
 
 Predictor       Coef       Stdev    t-ratio        p
 Constant       71.16       11.99       5.94    0.000
 C3            0.8360      0.2012       4.15    0.001
 
 s = 14.56       R-sq = 53.5%     R-sq(adj) = 50.4%

 MTB > regress c21 1 c20
 
 The regression equation is
 C21 = 0.00 + 0.509 C20
 
 Predictor       Coef       Stdev    t-ratio        p
 Constant       0.000       2.627       0.00    1.000
 C20           0.5092      0.1463       3.48    0.003
               ******matches multiple regression slope
 
 s = 10.83       R-sq = 44.7%     R-sq(adj) = 41.0%
 
Partial Regression Plot
 MTB > plot c21 c20 
 
C21-                                                  *
 20+                                         *
   -                                                        *
   -
   -                       *
   -                  *               *   **               *
  0+                                        *
   -                          *
   -     *                                 * *
   -                  *              *
   -
-20+
   -
   -
   -
   -    *
-40+
     --+---------+---------+---------+---------+---------+----C20     
     -36       -24       -12         0        12        24