### SAS Textbook Examples Applied Linear Statistical Models by Neter, Kutner, et. al. Chapter 4: Simultaneous Inferences and Other Topics in Regression Analysis

options nocenter nodate;
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;
Example of 90% Confidence Intervals for the regression parameter estimates, p. 154.
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
Using the Working-Hotelling procedure to obtain a family of estimates and confidence
intervals for mean working hours when X = 30, 65, 100 with a family confidence coefficient
of 0.90, p. 156-157.
data extra;
input x y;
cards;
30 .
65 .
100 .
;
run;
data temp;
set ch1tab01 extra;
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=.;
syh = sqrt( (stdi)**2 - &mse );
f = finv(.90, 2, &df);
w = sqrt( 2*f );
lower = yhat - w*syh;
upper = yhat + w*syh;
run;
proc print data = temp2;
var x yhat syh f w lower upper;
run; 
Obs     x       yhat       syh         f          w        lower      upper

1      30    169.472    16.9697    2.54929    2.25800    131.154    207.790
2      65    294.429     9.9176    2.54929    2.25800    272.035    316.823
3     100    419.386    14.2723    2.54929    2.25800    387.159    451.613
Using the Bonferroni procedure to obtain a family of estimates and confidence intervals for mean working hours when X = 30, 65, 100 with a family confidence coefficient of 0.90, p. 157.
data extra;
input x y;
cards;
30 .
65 .
100 .
;
run;
data temp;
set ch1tab01 extra;
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=.;
syh = sqrt( (stdi)**2 - &mse );
B = tinv( 1- (.1 /(2*3)), &df);
lower = yhat - B*syh;
upper = yhat + B*syh;
run;
proc print data = temp2;
var x yhat syh B lower upper;
run; 
Obs     x       yhat       syh         B        lower      upper

1      30    169.472    16.9697    2.26373    131.057    207.887
2      65    294.429     9.9176    2.26373    271.978    316.880
3     100    419.386    14.2723    2.26373    387.077    451.695
Simultaneous Prediction intervals for new observations, p. 158-159.
data extra;
input x y;
cards;
80 .
100 .
;
run;
data temp;
set ch1tab01 extra;
run;
proc reg data = temp noprint;
model y = x/ alpha=.1;
output out=temp1 p=yhat stdi=spred;
run;
quit;
data temp2;
set temp1;
if y=.;
s = sqrt( 2*finv(.95, 2, 23) );
B = tinv( 1 - (.05/(2*2)), 23) ;
lowers = yhat - s*spred;
uppers = yhat + s*spred;
lowerb = yhat - b*spred;
upperb = yhat + b*spred;
run;
proc print data = temp2;
var x yhat spred b lowerb upperb s lowers uppers;
run; 
Obs    x      yhat     spred       B       lowerb    upperb      s       lowers    uppersc

1     80   347.982   49.9110   2.39788   228.302   467.662   2.61615   217.407   478.557
2    100   419.386   50.8666   2.39788   297.414   541.358   2.61615   286.311   552.461
Inputting the Warehouse data, table 4.2, p. 161.
data ch4tab02;
input x y;
label x = 'Work'
y = 'Labor';
cards;
20  114
196  921
115  560
50  245
122  575
100  475
33  138
154  727
80  375
147  670
182  828
160  762
;
run;
Creating the interaction between X and Y, the X^2 and the predicted Y-hat values. The rest of table 4.2, p. 161.
data ch4tab02;
set ch4tab02;
xy = x*y;
xsq = x**2;
run;
proc reg data = ch4tab02 noprint;
model y = x /noint;
output out= temp p=yhat r=e;
run;
proc print data = temp (obs = 5);
run;
Obs     x      y       xy       xsq       yhat        e

1     20    114      2280      400     93.705    20.2945
2    196    921    180516    38416    918.314     2.6863
3    115    560     64400    13225    538.807    21.1935
4     50    245     12250     2500    234.264    10.7363
5    122    575     70150    14884    571.603     3.3966
Fig. 4.1 and calculations on p. 162.
goptions reset = all;

symbol v=dot h=.8 c=blue;
proc reg data = temp;
model y = x/ noint clb;
plot y*x;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: y Labor

NOTE: No intercept in model. R-Square is redefined.

Analysis of Variance

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

Model                     1        4191980        4191980    18762.5    <.0001
Error                    11     2457.65933      223.42358
Uncorrected Total        12        4194438

Root MSE             14.94736    R-Square     0.9994
Dependent Mean      532.50000    Adj R-Sq     0.9994
Coeff Var             2.80702

Parameter Estimates

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

x          Work        1      4.68527      0.03421   136.98    <.0001      4.60999      4.76056
The Calibration example p. 168 was not reproduced.

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