SAS Textbook Examples
Applied Linear Statistical Models by Neter, Kutner, et. al.
Chapter 7: Multiple Regression II

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Table 7.1, p. 261.
data ch7tab01;
  input X1 X2 X3 Y;
  label x1 = 'Triceps' 
        x2 = 'Thigh cir.'
	x3 = 'Midarm cir.'
         y = 'body fat';
  cards;
  19.5  43.1  29.1  11.9
  24.7  49.8  28.2  22.8
  30.7  51.9  37.0  18.7
  29.8  54.3  31.1  20.1
  19.1  42.2  30.9  12.9
  25.6  53.9  23.7  21.7
  31.4  58.5  27.6  27.1
  27.9  52.1  30.6  25.4
  22.1  49.9  23.2  21.3
  25.5  53.5  24.8  19.3
  31.1  56.6  30.0  25.4
  30.4  56.7  28.3  27.2
  18.7  46.5  23.0  11.7
  19.7  44.2  28.6  17.8
  14.6  42.7  21.3  12.8
  29.5  54.4  30.1  23.9
  27.7  55.3  25.7  22.6
  30.2  58.6  24.6  25.4
  22.7  48.2  27.1  14.8
  25.2  51.0  27.5  21.1
;
run;
Table 7.2, p. 262-263.
proc reg data = ch7tab01;
  model y = x1;
  model y = x2;
  model y = x1 x2;
  model y = x1-x3;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     1      352.26980      352.26980      44.30    <.0001
Error                    18      143.11970        7.95109
Corrected Total          19      495.38950

Root MSE              2.81977    R-Square     0.7111
Dependent Mean       20.19500    Adj R-Sq     0.6950
Coeff Var            13.96271

                                Parameter Estimates

                                    Parameter       Standard
Variable     Label          DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept       1       -1.49610        3.31923      -0.45      0.6576
X1           Triceps         1        0.85719        0.12878       6.66      <.0001

The REG Procedure
Model: MODEL2
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     1      381.96582      381.96582      60.62    <.0001
Error                    18      113.42368        6.30132
Corrected Total          19      495.38950

Root MSE              2.51024    R-Square     0.7710
Dependent Mean       20.19500    Adj R-Sq     0.7583
Coeff Var            12.43002

                                Parameter Estimates

                                    Parameter       Standard
Variable     Label          DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept       1      -23.63449        5.65741      -4.18      0.0006
X2           Thigh cir.      1        0.85655        0.11002       7.79      <.0001

The REG Procedure
Model: MODEL3
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     2      385.43871      192.71935      29.80    <.0001
Error                    17      109.95079        6.46769
Corrected Total          19      495.38950

Root MSE              2.54317    R-Square     0.7781
Dependent Mean       20.19500    Adj R-Sq     0.7519
Coeff Var            12.59305

                                Parameter Estimates

                                    Parameter       Standard
Variable     Label          DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept       1      -19.17425        8.36064      -2.29      0.0348
X1           Triceps         1        0.22235        0.30344       0.73      0.4737
X2           Thigh cir.      1        0.65942        0.29119       2.26      0.0369

The REG Procedure
Model: MODEL4
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     3      396.98461      132.32820      21.52    <.0001
Error                    16       98.40489        6.15031
Corrected Total          19      495.38950

Root MSE              2.47998    R-Square     0.8014
Dependent Mean       20.19500    Adj R-Sq     0.7641
Coeff Var            12.28017

                                Parameter Estimates

                                    Parameter       Standard
Variable     Label          DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept       1      117.08469       99.78240       1.17      0.2578
X1           Triceps         1        4.33409        3.01551       1.44      0.1699
X2           Thigh cir.      1       -2.85685        2.58202      -1.11      0.2849
X3           Midarm cir.     1       -2.18606        1.59550      -1.37      0.1896
Table 7.4, p. 267.
Test1 is for the example of testing one variable, p. 269.
Test2 is for the example of testing two variables at once, p. 270-271.
proc reg data = ch7tab01;
  model y = x1-x3/ss1;
  test1: test x3 = 0;
  test2: test x2=x3=0;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     3      396.98461      132.32820      21.52    <.0001
Error                    16       98.40489        6.15031
Corrected Total          19      495.38950

Root MSE              2.47998    R-Square     0.8014
Dependent Mean       20.19500    Adj R-Sq     0.7641
Coeff Var            12.28017

                                    Parameter Estimates

                                 Parameter      Standard
Variable    Label         DF      Estimate         Error   t Value   Pr > |t|     Type I SS

Intercept   Intercept      1     117.08469      99.78240      1.17     0.2578    8156.76050
X1          Triceps        1       4.33409       3.01551      1.44     0.1699     352.26980
X2          Thigh cir.     1      -2.85685       2.58202     -1.11     0.2849      33.16891
X3          Midarm cir.    1      -2.18606       1.59550     -1.37     0.1896      11.54590

The REG Procedure
Model: MODEL1

       Test test1 Results for Dependent Variable Y

                                Mean
Source             DF         Square    F Value    Pr > F

Numerator           1       11.54590       1.88    0.1896
Denominator        16        6.15031

The REG Procedure
Model: MODEL1

       Test test2 Results for Dependent Variable Y

                                Mean
Source             DF         Square    F Value    Pr > F

Numerator           2       22.35741       3.64    0.0500
Denominator        16        6.15031
Coefficients of partial determination, p. 275.
ry1.2 and ry2.1 are from the first model.
ry3.12 is the coef. from X3 in the second model.
proc reg data = ch7tab01;
  model y = x1 x2 / pcorr2;
  model y = x1-x3 / pcorr2;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     2      385.43871      192.71935      29.80    <.0001
Error                    17      109.95079        6.46769
Corrected Total          19      495.38950

Root MSE              2.54317    R-Square     0.7781
Dependent Mean       20.19500    Adj R-Sq     0.7519
Coeff Var            12.59305

                                    Parameter Estimates

                                                                                     Squared
                                 Parameter      Standard                             Partial
Variable    Label         DF      Estimate         Error   t Value   Pr > |t|   Corr Type II

Intercept   Intercept      1     -19.17425       8.36064     -2.29     0.0348              .
X1          Triceps        1       0.22235       0.30344      0.73     0.4737        0.03062
X2          Thigh cir.     1       0.65942       0.29119      2.26     0.0369        0.23176

The REG Procedure
Model: MODEL2
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     3      396.98461      132.32820      21.52    <.0001
Error                    16       98.40489        6.15031
Corrected Total          19      495.38950

Root MSE              2.47998    R-Square     0.8014
Dependent Mean       20.19500    Adj R-Sq     0.7641
Coeff Var            12.28017

                                    Parameter Estimates

                                                                                     Squared
                                 Parameter      Standard                             Partial
Variable    Label         DF      Estimate         Error   t Value   Pr > |t|   Corr Type II

Intercept   Intercept      1     117.08469      99.78240      1.17     0.2578              .
X1          Triceps        1       4.33409       3.01551      1.44     0.1699        0.11435
X2          Thigh cir.     1      -2.85685       2.58202     -1.11     0.2849        0.07108
X3          Midarm cir.    1      -2.18606       1.59550     -1.37     0.1896        0.10501
Inputting the Dwaine Studio Data from Ch. 6, Table 5 (p. 241).
data ch6fig05;
  input x1 x2 y;
  label y  = 'sales'
        x1 = 'targtpop'
        x2 = 'dispoinc';
cards;
  68.5  16.7  174.4
  45.2  16.8  164.4
  91.3  18.2  244.2
  47.8  16.3  154.6
  46.9  17.3  181.6
  66.1  18.2  207.5
  49.5  15.9  152.8
  52.0  17.2  163.2
  48.9  16.6  145.4
  38.4  16.0  137.2
  87.9  18.3  241.9
  72.8  17.1  191.1
  88.4  17.4  232.0
  42.9  15.8  145.3
  52.5  17.8  161.1
  85.7  18.4  209.7
  41.3  16.5  146.4
  51.7  16.3  144.0
  89.6  18.1  232.6
  82.7  19.1  224.1
  52.3  16.0  166.5
  ;
run;
Creating the standardized variables of the Dwaine Studios Data, p. 282.
proc sql; 
  create table temp as
  select *, ( y - mean(y) )/( std(y)*( sqrt( count(y)-1 ) ) ) as yprime,
            ( x1 - mean(x1) )/( std(x1)*( sqrt( count(x1)-1 ) ) ) as x1prime,
            ( x2 - mean(x2) )/( std(x2)*( sqrt( count(x2)-1 ) ) ) as x2prime
  from ch6fig05;
quit;
Table 7.5a, p. 283.
proc print data = temp (obs= 10);
  var y x1 x2;
run;
proc means data = temp mean std ;
  var y x1 x2;
run;
Obs      y       x1      x2

  1    174.4    68.5    16.7
  2    164.4    45.2    16.8
  3    244.2    91.3    18.2
  4    154.6    47.8    16.3
  5    181.6    46.9    17.3
  6    207.5    66.1    18.2
  7    152.8    49.5    15.9
  8    163.2    52.0    17.2
  9    145.4    48.9    16.6
 10    137.2    38.4    16.0
 
The MEANS Procedure

Variable    Label               Mean         Std Dev
----------------------------------------------------
y           sales        181.9047619      36.1913039
x1          targtpop      62.0190476      18.6203281
x2          dispoinc      17.1428571       0.9703460
----------------------------------------------------
Table 7.5b, p. 283.
proc print data = temp;
  var yprime x1prime x2prime;
run;
Obs     yprime      x1prime     x2prime

  1    -0.04637     0.07783    -0.10205
  2    -0.10815    -0.20198    -0.07901
  3     0.38489     0.35163     0.24361
  4    -0.16870    -0.17075    -0.19423
  5    -0.00188    -0.18156     0.03621
  6     0.15814     0.04901     0.24361
  7    -0.17982    -0.15034    -0.28640
  8    -0.11557    -0.12032     0.01317
  9    -0.22554    -0.15754    -0.12510
 10    -0.27621    -0.28364    -0.26336
 11     0.37068     0.31080     0.26665
 12     0.05681     0.12947    -0.00988
 13     0.30951     0.31680     0.05926
 14    -0.22616    -0.22960    -0.30945
 15    -0.12854    -0.11431     0.15143
 16     0.17173     0.28438     0.28970
 17    -0.21937    -0.24881    -0.14814
 18    -0.23419    -0.12392    -0.19423
 19     0.31322     0.33121     0.22056
 20     0.26070     0.24835     0.45100
 21    -0.09518    -0.11671    -0.26336
Table 7.5c, p. 283.
proc reg data = temp;
  model yprime = x1prime x2prime;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: yprime

                             Analysis of Variance

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

Model                     2        0.91675        0.45837      99.10    <.0001
Error                    18        0.08325        0.00463
Corrected Total          20        1.00000

Root MSE              0.06801    R-Square     0.9167
Dependent Mean    3.23815E-17    Adj R-Sq     0.9075
Coeff Var         2.100236E17

                        Parameter Estimates

                     Parameter       Standard
Variable     DF       Estimate          Error    t Value    Pr > |t|

Intercept     1    -8.9542E-18        0.01484      -0.00      1.0000
x1prime       1        0.74837        0.10896       6.87      <.0001
x2prime       1        0.25110        0.10896       2.30      0.0333
Inputting the data of the Work Crew data.
data ch7tab06;
  input x1 x2 y;
  label x1 = 'Crew size'
        x2 = 'Bonus Pay'
         y = 'Crew productivity';
cards;
  4  2  42
  4  2  39
  4  3  48
  4  3  51
  6  2  49
  6  2  53
  6  3  61
  6  3  60
;
run;
Table 7.6, p. 286.
proc print data = ch7tab06;
run;
Obs    x1    x2     y

 1      4     2    42
 2      4     2    39
 3      4     3    48
 4      4     3    51
 5      6     2    49
 6      6     2    53
 7      6     3    61
 8      6     3    60
Table 7.7, p. 287.
proc reg data = ch7tab06;
  model y = x1 x2;
  model y = x1;
  model y = x2;
run;
The REG Procedure
Model: MODEL1
Dependent Variable: y Crew productivity

                             Analysis of Variance

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

Model                     2      402.25000      201.12500      57.06    0.0004
Error                     5       17.62500        3.52500
Corrected Total           7      419.87500

Root MSE              1.87750    R-Square     0.9580
Dependent Mean       50.37500    Adj R-Sq     0.9412
Coeff Var             3.72704

                                   Parameter Estimates

                                          Parameter       Standard
Variable     Label                DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept             1        0.37500        4.74045       0.08      0.9400
x1           Crew size             1        5.37500        0.66380       8.10      0.0005
x2           Bonus Pay             1        9.25000        1.32759       6.97      0.0009

The REG Procedure
Model: MODEL2
Dependent Variable: y Crew productivity

                             Analysis of Variance

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

Model                     1      231.12500      231.12500       7.35    0.0351
Error                     6      188.75000       31.45833
Corrected Total           7      419.87500

Root MSE              5.60877    R-Square     0.5505
Dependent Mean       50.37500    Adj R-Sq     0.4755
Coeff Var            11.13404

                                   Parameter Estimates

                                          Parameter       Standard
Variable     Label                DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept             1       23.50000       10.11136       2.32      0.0591
x1           Crew size             1        5.37500        1.98300       2.71      0.0351

The REG Procedure
Model: MODEL3
Dependent Variable: y Crew productivity

                             Analysis of Variance

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

Model                     1      171.12500      171.12500       4.13    0.0885
Error                     6      248.75000       41.45833
Corrected Total           7      419.87500

Root MSE              6.43881    R-Square     0.4076
Dependent Mean       50.37500    Adj R-Sq     0.3088
Coeff Var            12.78177

                                   Parameter Estimates

                                          Parameter       Standard
Variable     Label                DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept             1       27.25000       11.60774       2.35      0.0572
x2           Bonus Pay             1        9.25000        4.55293       2.03      0.0885
Fig. 7.3, p. 290. The scatter macro can be used for making a scatterplot matrix.
%scatter(data = Ch7tab01, var = x1 x2 x3);
Showing correlations of x1 to x3.
proc corr data = ch7tab01;
  var x1-x3;
run;
The CORR Procedure

   3  Variables:    X1       X2       X3

                                     Simple Statistics

Variable         N        Mean     Std Dev         Sum     Minimum     Maximum  Label

X1              20    25.30500     5.02326   506.10000    14.60000    31.40000  Triceps
X2              20    51.17000     5.23461        1023    42.20000    58.60000  Thigh cir.
X3              20    27.62000     3.64715   552.40000    21.30000    37.00000  Midarm cir.

      Pearson Correlation Coefficients, N = 20
             Prob > |r| under H0: Rho=0

                       X1            X2            X3

X1                1.00000       0.92384       0.45778
Triceps                          <.0001        0.0424

X2                0.92384       1.00000       0.08467
Thigh cir.         <.0001                      0.7227

X3                0.45778       0.08467       1.00000
Midarm cir.        0.0424        0.7227
Inputting data in table 7.9, p. 302.
data ch7tab09;
  input y x1 x2;
  label  y = 'cycles'
        x1 = 'Charge rate'
	x2 = 'Temperature';
cards;
  150  0.6  10
   86  1.0  10
   49  1.4  10
  288  0.6  20
  157  1.0  20
  131  1.0  20
  184  1.0  20
  109  1.4  20
  279  0.6  30
  235  1.0  30
  224  1.4  30
;
run;
* Recoding the variables. ;
proc sql; 
  create table temp as
  select *, (x1-mean(x1))/.4 as lx1, (x2-mean(x2))/10 as lx2,
            ((x1-mean(x1))/.4)*((x1-mean(x1))/.4) as lx1sq, 
            ((x2-mean(x2))/10)*((x2-mean(x2))/10) as lx2sq, 
            ((x1-mean(x1))/.4)*((x2-mean(x2))/10) as lx1x2, 
            x1*x1 as x1sq, x2*x2 as x2sq
  from ch7tab09;
quit;
Correlations at the bottom of p. 302.
proc corr data = temp;
  var x1 x1sq x2 x2sq lx1 lx1sq lx2 lx2sq;
run;
The CORR Procedure

   8  Variables:    x1       x1sq     x2       x2sq     lx1      lx1sq    lx2      lx2sq

                                     Simple Statistics

Variable         N        Mean     Std Dev         Sum     Minimum     Maximum  Label

x1              11     1.00000     0.30984    11.00000     0.60000     1.40000  Charge rate
x1sq            11     1.08727     0.62529    11.96000     0.36000     1.96000
x2              11    20.00000     7.74597   220.00000    10.00000    30.00000  Temperature
x2sq            11   454.54545   314.20896        5000   100.00000   900.00000
lx1             11           0     0.77460           0    -1.00000     1.00000
lx1sq           11     0.54545     0.52223     6.00000           0     1.00000
lx2             11           0     0.77460           0    -1.00000     1.00000
lx2sq           11     0.54545     0.52223     6.00000           0     1.00000

                         Pearson Correlation Coefficients, N = 11
                                Prob > |r| under H0: Rho=0

                   x1      x1sq        x2      x2sq       lx1     lx1sq       lx2     lx2sq

x1            1.00000   0.99103   0.00000   0.00000   1.00000   0.00000   0.00000   0.00000
Charge rate              <.0001    1.0000    1.0000    <.0001    1.0000    1.0000    1.0000

x1sq          0.99103   1.00000   0.00000   0.00592   0.99103   0.13363   0.00000   0.03563
               <.0001              1.0000    0.9862    <.0001    0.6953    1.0000    0.9172

x2            0.00000   0.00000   1.00000   0.98609   0.00000   0.00000   1.00000   0.00000
Temperature    1.0000    1.0000              <.0001    1.0000    1.0000    <.0001    1.0000

x2sq          0.00000   0.00592   0.98609   1.00000   0.00000   0.04432   0.98609   0.16621
               1.0000    0.9862    <.0001              1.0000    0.8970    <.0001    0.6253

lx1           1.00000   0.99103   0.00000   0.00000   1.00000   0.00000   0.00000   0.00000
               <.0001    <.0001    1.0000    1.0000              1.0000    1.0000    1.0000

lx1sq         0.00000   0.13363   0.00000   0.04432   0.00000   1.00000   0.00000   0.26667
               1.0000    0.6953    1.0000    0.8970    1.0000              1.0000    0.4280

lx2           0.00000   0.00000   1.00000   0.98609   0.00000   0.00000   1.00000   0.00000
               1.0000    1.0000    <.0001    <.0001    1.0000    1.0000              1.0000

lx2sq         0.00000   0.03563   0.00000   0.16621   0.00000   0.26667   0.00000   1.00000
               1.0000    0.9172    1.0000    0.6253    1.0000    0.4280    1.0000
Table 7.9, p. 303.
proc print data = temp;
run;
proc means data = temp mean;
  var x1 x2;
run;
Obs     y      x1    x2    lx1    lx2    lx1sq    lx2sq    lx1x2    x1sq    x2sq

  1    150    0.6    10     -1     -1      1        1         1     0.36     100
  2     86    1.0    10      0     -1      0        1        -0     1.00     100
  3     49    1.4    10      1     -1      1        1        -1     1.96     100
  4    288    0.6    20     -1      0      1        0         0     0.36     400
  5    157    1.0    20      0      0      0        0         0     1.00     400
  6    131    1.0    20      0      0      0        0         0     1.00     400
  7    184    1.0    20      0      0      0        0         0     1.00     400
  8    109    1.4    20      1      0      1        0         0     1.96     400
  9    279    0.6    30     -1      1      1        1        -1     0.36     900
 10    235    1.0    30      0      1      0        1         0     1.00     900
 11    224    1.4    30      1      1      1        1         1     1.96     900
 
The MEANS Procedure

Variable    Label                  Mean
---------------------------------------
x1          Charge rate       1.0000000
x2          Temperature      20.0000000
---------------------------------------
Table 7.7, p. 304.
Fig. 7.8a-7.8c, p. 304.
Test1 is the Partial F-test on p. 306.
proc reg data = temp;
  model y = lx1 lx2 lx1sq lx2sq lx1x2/ss1;
  plot r.*p. r.*lx1 r.*lx2;
  output out=tempout p=fitted r=residual;
  test lx1sq=lx2sq=lx1x2=0;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y cycles

                             Analysis of Variance

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

Model                     5          55366          11073      10.57    0.0109
Error                     5     5240.43860     1048.08772
Corrected Total          10          60606

Root MSE             32.37418    R-Square     0.9135
Dependent Mean      172.00000    Adj R-Sq     0.8271
Coeff Var            18.82220

                                      Parameter Estimates

                                  Parameter       Standard
Variable     Label        DF       Estimate          Error    t Value    Pr > |t|      Type I SS

Intercept    Intercept     1      162.84211       16.60761       9.81      0.0002         325424
lx1                        1      -55.83333       13.21670      -4.22      0.0083          18704
lx2                        1       75.50000       13.21670       5.71      0.0023          34202
lx1sq                      1       27.39474       20.34008       1.35      0.2359     1645.96667
lx2sq                      1      -10.60526       20.34008      -0.52      0.6244      284.92807
lx1x2                      1       11.50000       16.18709       0.71      0.5092      529.00000

The REG Procedure

         Test 1 Results for Dependent Variable y

                                Mean
Source             DF         Square    F Value    Pr > F

Numerator           3      819.96491       0.78    0.5527
Denominator         5     1048.08772
Fig. 7.8a, p. 304.
Fig. 7.8b, p. 304.
Fig. 7.8c, p. 304.
Fig. 7.8d, p. 304.
proc univariate data = tempout noprint;
  qqplot residual/ normal;
run;
First Order Models using transformed and not transformed variables, p. 306. The CLB option provides the confidence limits for the parameters on p. 307.
proc reg data = temp;
  model y = lx1 lx2;
  model y = x1 x2/ clb;
  output out=tempout p=fitted;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y cycles

                             Analysis of Variance

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

Model                     2          52906          26453      27.48    0.0003
Error                     8     7700.33333      962.54167
Corrected Total          10          60606

Root MSE             31.02486    R-Square     0.8729
Dependent Mean      172.00000    Adj R-Sq     0.8412
Coeff Var            18.03771

                                Parameter Estimates

                                    Parameter       Standard
Variable     Label          DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept       1      172.00000        9.35435      18.39      <.0001
lx1                          1      -55.83333       12.66584      -4.41      0.0023
lx2                          1       75.50000       12.66584       5.96      0.0003

The REG Procedure
Model: MODEL2
Dependent Variable: y cycles

                             Analysis of Variance

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

Model                     2          52906          26453      27.48    0.0003
Error                     8     7700.33333      962.54167
Corrected Total          10          60606

Root MSE             31.02486    R-Square     0.8729
Dependent Mean      172.00000    Adj R-Sq     0.8412
Coeff Var            18.03771

                                Parameter Estimates

                                    Parameter       Standard
Variable     Label          DF       Estimate          Error    t Value    Pr > |t|

Intercept    Intercept       1      160.58333       41.61545       3.86      0.0048
x1           Charge rate     1     -139.58333       31.66461      -4.41      0.0023
x2           Temperature     1        7.55000        1.26658       5.96      0.0003

                    Parameter Estimates

Variable     Label          DF       95% Confidence Limits

Intercept    Intercept       1       64.61793      256.54874
x1           Charge rate     1     -212.60206      -66.56461
x2           Temperature     1        4.62925       10.47075
Fig. 7.9, p. 307.
We are using the fitted values from the last model in the previous proc reg.
proc g3d data = tempout;
  plot  x2*x1 =  fitted  ;
  label fitted = 'Number of Cycles'
            x1 = 'Charge Rate'
            x2 = 'Temperature';
run;
We cannot find the data files for section 7.8, pages 308-313. The 3d graphs can be made using 3D Graphs using SAS and SAS Teaching Tools- Graphs for Visualizing Interactions of Continuous Variables in Multiple Regression.
Creating centered variables for the Body Fat dataset from table 7.1, p. 261.
proc sql; 
  create table temp as
  select *,  y - mean(y) as cy, x1 - mean(x1) as cx1,
			 x2 - mean(x2) as cx2,  x3 - mean(x3) as cx3
  from ch7tab01;
quit;
data temp;
  set temp;
  cx1x2 = cx1*cx2;
  cx1x3 = cx1*cx3;
  cx2x3 = cx2*cx3;
run;
Fitting the Regression model (7.93), p. 315. The SS1 option lets you obtain the extra sums of squares. Test1 is the test of the interaction terms.
proc reg data = temp;
  model y = cx1 cx2 cx3 cx1x2 cx1x3 cx2x3/ss1;
  test1: test cx1x2 = cx1x3 = cx2x3 = 0;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: Y body fat

                             Analysis of Variance

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

Model                     6      407.69950       67.94992      10.07    0.0003
Error                    13       87.69000        6.74538
Corrected Total          19      495.38950

Root MSE              2.59719    R-Square     0.8230
Dependent Mean       20.19500    Adj R-Sq     0.7413
Coeff Var            12.86055

                                      Parameter Estimates

                                  Parameter       Standard
Variable     Label        DF       Estimate          Error    t Value    Pr > |t|      Type I SS

Intercept    Intercept     1       20.52689        1.07363      19.12      <.0001     8156.76050
cx1                        1        3.43781        3.57867       0.96      0.3543      352.26980
cx2                        1       -2.09472        3.03677      -0.69      0.5025       33.16891
cx3                        1       -1.61634        1.90721      -0.85      0.4121       11.54590
cx1x2                      1        0.00888        0.03085       0.29      0.7781        1.49572
cx1x3                      1       -0.08479        0.07342      -1.15      0.2689        2.70433
cx2x3                      1        0.09042        0.09200       0.98      0.3437        6.51484

The REG Procedure
Model: MODEL1

       Test test1 Results for Dependent Variable Y

                                Mean
Source             DF         Square    F Value    Pr > F

Numerator           3        3.57163       0.53    0.6699
Denominator        13        6.74538

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