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SAS Textbook Examples
Applied Linear Statistical Models by Neter, Kutner, et. al.
Chapter 2: Inferences in Regression Analysis

Inputting the Toluca Company data.
data ch1tab01;
  input x y;
  label x = 'Lot Size'
        y = 'Work Hrs';
cards;
   80  399
   30  121
   50  221
   90  376
   70  361
   60  224
  120  546
   80  352
  100  353
   50  157
   40  160
   70  252
   90  389
   20  113
  110  435
  100  420
   30  212
   50  268
   90  377
  110  421
   30  273
   90  468
   40  244
   80  342
   70  323
;
run;
Table 2.1 and Fig. 2.2, p. 50-51.
proc reg data = ch1tab01;
  model y = x/ clb;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y Work Hrs

                             Analysis of Variance

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

Model                     1         252378         252378     105.88    <.0001
Error                    23          54825     2383.71562
Corrected Total          24         307203


Root MSE             48.82331    R-Square     0.8215
Dependent Mean      312.28000    Adj R-Sq     0.8138
Coeff Var            15.63447

                                      Parameter Estimates

                            Parameter     Standard
Variable   Label      DF     Estimate        Error  t Value  Pr > |t|    95% Confidence Limits

Intercept  Intercept   1     62.36586     26.17743     2.38    0.0259      8.21371    116.51801
x          Lot Size    1      3.57020      0.34697    10.29    <.0001      2.85244      4.28797
90% CI for beta0, p. 54.
proc reg data = ch1tab01;
  model y = x/ clb alpha=.1;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y Work Hrs

                             Analysis of Variance

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

Model                     1         252378         252378     105.88    <.0001
Error                    23          54825     2383.71562
Corrected Total          24         307203

Root MSE             48.82331    R-Square     0.8215
Dependent Mean      312.28000    Adj R-Sq     0.8138
Coeff Var            15.63447

                                      Parameter Estimates

                            Parameter     Standard
Variable   Label      DF     Estimate        Error  t Value  Pr > |t|    90% Confidence Limits

Intercept  Intercept   1     62.36586     26.17743     2.38    0.0259     17.50110    107.23062
x          Lot Size    1      3.57020      0.34697    10.29    <.0001      2.97554      4.16487
Predicting the mean of 3 new observations given a X = 100, p. 66-67.
data temp;
  if _n_ = 1 then x = 100;
  output;
  set ch1tab01;
run;
ods listing close;
ods output anova=out;
proc reg data = temp;
  model y = x/ alpha=.1;
  output out=temp1 p=yhat stdi=stdi;
run;
quit;
ods listing;
data _null_;
  set out;
  if source = 'Error' then do;
  call symput ('mse', ms);
  call symput ('df', df );
  end;
run;
%put &mse &df; /* To see the value of MSE and df in the log file. */ 
data temp2;
  set temp1;
  if y=.;
  spred = sqrt( stdi**2 - (2/3)*&mse);
  t = tinv(.95, &df);
  lower = yhat - t*spred;
  upper = yhat + t*spred;
run;
proc print data = temp2;
  var x yhat spred t lower upper;
run;
Obs      yhat      lower      upper

  9    419.386    332.207    506.565
Estimating 90% confidence interval for the mean response E{Yh} when X = 65, p. 60.
data temp;
  if _n_ = 1 then x=65; output;
  set ch1tab01;
run;
proc reg data = temp noprint;
  model y = x/ alpha=.1;
  output out=temp1 lclm=lower uclm=upper p=yhat;
run;
quit;
proc print data = temp1;
  where x=65;
  var yhat lower upper;
run;
Obs      yhat      lower      upper

  1    294.429    277.432    311.426
Estimating 90% confidence interval for the mean response E{Yh} when X=100, p. 60.
data temp;
  if _n_ = 1 then x=100; output;
  set ch1tab01;
run;
proc reg data = temp noprint;
  model y = x/ alpha=.1;
  output out=temp1 lclm=lower uclm=upper p=yhat ;
run;
quit;
proc sort data = temp1;
  by x;
run;
data temp1;
  set temp1;
  by x;
  if first.x;
run;
proc print data = temp1;
  where x=100;
  var yhat lower upper;
run;
Obs      yhat      lower      upper

  9    419.386    394.925    443.847
Estimating a 90% confidence interval for a new predicted value when X=100, p. 65.
data temp;
  if _n_ = 1 then x=100; output;
  set ch1tab01;
run;
proc reg data = temp noprint;
  model y = x/ alpha=.1;
  output out=temp1 lcl=lower ucl=upper p=yhat stdi=stdi;
run;
quit;
proc sort data = temp1;
  by x;
run;
data temp1;
  set temp1;
  by x;
  if first.x;
run;
proc print data = temp1;
  where x=100;
  var yhat stdi lower upper;
run;
Obs      yhat       stdi      lower      upper

  9    419.386    50.8666    332.207    506.565
Example Confidence Bands including Fig. 2.6, p. 68-69.
proc reg data = ch1tab01 noprint;
  model y = x;
  output out = temp stdp=stdp p=p;
run;
data temp1;
  set temp;
  lbound = p - 2.258*stdp;
  ubound = p + 2.258*stdp;
run;
proc sort data = temp1;
  by x;
run;
 
symbol1 v=none i=join c=red;
symbol2 v=none i=join c=red;
proc gplot data = temp1;
  plot (ubound lbound)*x / overlay;
run;
quit;
Example of correlation coefficient and R-squared, p. 82.
proc corr data = ch1tab01;
 var x y;
run;
proc reg data = ch1tab01;
  model y =x;
run;
quit;
The CORR Procedure

   2  Variables:    x        y

                                       Simple Statistics

Variable          N         Mean      Std Dev          Sum      Minimum      Maximum   Label

x                25     70.00000     28.72281         1750     20.00000    120.00000   Lot Size
y                25    312.28000    113.13764         7807    113.00000    546.00000   Work Hrs

Pearson Correlation Coefficients, N = 25
       Prob > |r| under H0: Rho=0

                     x             y

x              1.00000       0.90638
Lot Size                      <.0001

y              0.90638       1.00000
Work Hrs        <.0001

The REG Procedure
Model: MODEL1
Dependent Variable: y Work Hrs

                             Analysis of Variance

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

Model                     1         252378         252378     105.88    <.0001
Error                    23          54825     2383.71562
Corrected Total          24         307203

Root MSE             48.82331    R-Square     0.8215
Dependent Mean      312.28000    Adj R-Sq     0.8138
Coeff Var            15.63447

                               Parameter Estimates

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

Intercept    Intercept     1       62.36586       26.17743       2.38      0.0259
x            Lot Size      1        3.57020        0.34697      10.29      <.0001

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