STAT512
Analysis of Covariance
Example 1:
title3 "With Covariate the Age of the Individual";
data ancova;
input age oxygen treatment $;
cards;
31 17.05 aerobic
23
4.96 aerobic
27 10.40 aerobic
28 11.05 aerobic
22
0.26 aerobic
24
2.51 aerobic
23 -0.87 running
22 -10.74 running
22 -3.27 running
25 -1.97 running
27
7.50 running
20 -7.25 running
;
proc print data = ancova;
run;
title4 "Model With an Interation";
proc glm data = ancova;
class treatment;
model oxygen = treatment age treatment*age / solution;
output out=new p=pred r=resid;
means treatment/hovtest=bf;
*beware don't interpret it here if when we have an interaction just look at
Brown Forsythe test;
run;
*do residual analysis as usual with resid and pred;
proc capability data=new;
var resid;
qqplot;
histogram;
run;
proc gplot data=new;
plot resid*pred;
run;
title4 "Model Without an Interation";
proc glm data = ancova;
class treatment;
model oxygen = treatment age / solution;
lsmeans treatment / pdiff stderr ;
output out=new1 p=pred r=resid;
means treatment/hovtest=bf;
*beware don't interpret it here if when we have an interaction just look at
Brown Forsythe test;
run;
*do residual analysis as usual with resid and pred;
proc capability data=new1;
var resid;
qqplot;
histogram;
run;
proc gplot data=new1;
plot resid*pred;
run;
run;
*Using regression with dummy variables use SS III ;
title4 "Using Regression with dummy variables";
data dummy;
set ancova;
if treatment="aerobic" then trt_dummy=1;
else trt_dummy=0;
int=age*trt_dummy;
run;
proc reg data=dummy;
model oxygen= age trt_dummy int;
output out=new2 p=pred r=resid;
run;
*do residual analysis as usual with resid and pred;
proc capability data=new2;
var resid;
qqplot;
histogram;
run;
proc gplot data=new2;
plot resid*pred;
run;
run;
proc glm data=dummy;
model oxygen= age trt_dummy trt_dummy*age;
output out=new3 p=pred r=resid;
means treatment/hovtest=bf;
*beware don't interpret it here if when we have an interaction just look at
Brown Forsythe test;
run;
*do residual analysis as usual with resid and pred;
proc capability data=new3;
var resid;
qqplot;
histogram;
run;
proc gplot data=new3;
plot resid*pred;
run;
Example 2:
data cars;
input Price Mileage
Make $;
datalines;
17314.1
8221 Buick
17542.0
9135 Buick
16218.8
13196 Buick
16336.9
16342 Buick
16339.2
19832 Buick
15709.1
22236 Buick
15048.0
22964 Buick
14862.1
24021 Buick
15295.0
27325 Buick
21335.9
10237 Buick
12649.1
3629 Chevrolet
12314.6
4142 Chevrolet
11318.0
11156 Chevrolet
12409.9
11981 Chevrolet
11555.3
13404 Chevrolet
11700.1
15253 Chevrolet
11215.0
19945 Chevrolet
10145.0
23963 Chevrolet
9954.1
37345 Chevrolet
11918.5
7278 Chevrolet
25452.5
11892 Pontiac
23449.3
17273 Pontiac
23578.2
19148 Pontiac
22525.3
19521 Pontiac
21982.6
20472 Pontiac
22231.6
21929 Pontiac
22189.1
25651 Pontiac
21765.1
25794 Pontiac
21403.8
27168 Pontiac
21200.7
31197 Pontiac
26337.8
16068 SAAB
26775.0
16688 SAAB
25300.0
19569 SAAB
24896.6
21266 SAAB
25996.8
21433 SAAB
24801.6
26345 SAAB
24063.0
27674 SAAB
23249.8
27686 SAAB
19244.9
30387 SAAB
26841.1
10003 SAAB
;
proc gplot data=cars;
plot price*mileage=make;
run;
proc glm data=cars;
class make;
model price=make mileage make*mileage/solution;
estimate "buick-chevy" make 1 -1 0 0 mileage 20000;
estimate "buick-Pon" make 1 0 -1 0 mileage 20000;
estimate "saab-Pon" make 0 -1 0 -1 mileage 20000;
estimate "saab-chevy" make 0 -1 0 -1 mileage 20000;
lsmeans make/adjust=tukey;
output out=new r=resid p=pred;
run;
proc capability data=new;
var resid;
qqplot;
histogram;
run;
proc gplot data=new;
plot resid*pred;
run;
run;data dummy;
set cars;
if make="Buick" then x1=1;
else x1=0;
if make="Pontiac" then x2=1;
else x2=0;
if make="SAAB" then x3=1;
else x3=0;
x4=mileage;
x5=x1*x4;
x6=x2*x4;
x7=x3*x4;
run;
proc reg data=dummy;
model price = x1 x2 x3 x4 x5 x6 x7;
run;