Polynomial Regression Using SAS
/*Read in the SPSS portable file using Proc Convert*/
filename file1 "d:\510\2007\data\htwt.por";
proc convert spss=file1 out=htwt;
run;
options pageno=1;
OPTIONS FORMCHAR="|----|+|---+=|-/\<>*";
title;
proc contents data=htwt;
run;
Data Set Name
Member Type
Engine
Created
Last Modified
Protection
Data Set Type
Label
Data Representation
Encoding
The CONTENTS Procedure
WORK.HTWT
DATA
V9
Monday, February 05, 2007 04:41:38 PM
Monday, February 05, 2007 04:41:38 PM
Observations
Variables
Indexes
Observation Length
Deleted Observations
Compressed
Sorted
WINDOWS_32
wlatin1 Western (Windows)
Engine/Host Dependent Information
Data Set Page Size
4096
Number of Data Set Pages
3
First Data Page
1
Max Obs per Page
126
Obs in First Data Page
83
Number of Data Set Repairs 0
File Name
c:\temp\_TD2040\htwt.sas7bdat
Release Created
9.0101M2
Host Created
XP_PRO
Alphabetic List of Variables and Attributes
#
2
3
1
4
Variable
AGE
HEIGHT
SEX
WEIGHT
Type
Num
Num
Char
Num
Len
8
8
8
8
Format
5.2
5.2
8.
6.2
1
237
4
0
32
0
NO
NO
proc means data=htwt;
run;
The MEANS Procedure
Variable
N
Mean
Std Dev
Minimum
Maximum
------------------------------------------------------------------------------AGE
237
16.4430380
1.8425767
13.9000000
25.0000000
HEIGHT
237
61.3645570
3.9454019
50.5000000
72.0000000
WEIGHT
237
101.3080169
19.4406980
50.5000000
171.5000000
-------------------------------------------------------------------------------
goptions reset=all;
goptions device=win target=winprtm;
symbol1 color=black value=dot height=.5 interpol=rq;
title "Scatter Plot with Quadratic Regression Line";
proc gplot data=htwt;
where age < 20;
plot height * age ;
run;
/*Data Step to Create Age-Squared, Centered Age, and Centered Age-Squared*/
data htwt2;
set htwt;
agesq = age*age;
centage = age - 16.3;
centagesq = centage*centage;
run;
title "Regression Model with Original Age and Age-Squared Variables";
proc reg data=htwt2;
2
where age < 20;
model height = age agesq;
plot rstudent.*predicted.;
output out=regdata1 p=predict r=resid rstudent=rstudent;
run; quit;
Regression Model with Original Age and Age-Squared Variables
The REG Procedure
Model: MODEL1
Dependent Variable: HEIGHT
Number of Observations Read
Number of Observations Used
Source
Model
Error
Corrected Total
DF
2
227
229
Root MSE
Dependent Mean
Coeff Var
Variable
Intercept
AGE
agesq
DF
1
1
1
230
230
Analysis of Variance
Sum of
Mean
Squares
Square
1436.79524
718.39762
1940.95820
8.55048
3377.75343
2.92412
61.18739
4.77896
R-Square
Adj R-Sq
Parameter Estimates
Parameter
Standard
Estimate
Error
-31.22120
22.20249
9.83820
2.70952
-0.25318
0.08199
F Value
84.02
0.4254
0.4203
t Value
-1.41
3.63
-3.09
3
Pr > F
<.0001
Pr > |t|
0.1610
0.0003
0.0023
proc univariate data=regdata1;
var rstudent;
histogram;
qqplot / normal(mu=est sigma=est);
run;
title "Regression Model with Centered Age and Age-Squared Variables";
proc reg data=htwt2;
where age < 20;
model height = centage centagesq;
run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: HEIGHT
Number of Observations Read
Number of Observations Used
230
230
Analysis of Variance
DF
2
227
229
Sum of
Squares
1436.79524
1940.95820
3377.75343
Root MSE
Dependent Mean
Coeff Var
2.92412
61.18739
4.77896
Source
Model
Error
Corrected Total
Variable
Intercept
centage
centagesq
DF
1
1
1
Mean
Square
718.39762
8.55048
R-Square
Adj R-Sq
Parameter Estimates
Parameter
Standard
Estimate
Error
61.87284
0.29323
1.58438
0.12233
-0.25318
0.08199
F Value
84.02
0.4254
0.4203
t Value
211.00
12.95
-3.09
4
Pr > F
<.0001
Pr > |t|
<.0001
<.0001
0.0023