Exploring Female Body Weight using Multiple Linear Regression

This is a mini project from my linear model course.
1. Introduction
Human Body weight varies according to different human group. In this project; we are interested in human body weight in female within the age of 27. A weight equation for the female group in terms of body builds variables was found using multiple regression technique. Also series of T test have been executed to verify the relative significant importance of each variable, determining variable entries. The whole procedure can be described as follow figure1-1.
2. Procedure

3. Data

The initial measurements were taken at San Jose State University and at the U.S. Naval Postgraduate School in Monterey, California. These were primarily female individuals with in 27 years old, all physically active (several hours of exercise a week). Nine skeletal measurements (diameter measurements) were included in the study. Twelve girth (or circumference) measurements are used in the study. They, in contrast to skeletal (diameter) measurements, are not fixed over time except for the three "bony" girths of the wrist, knee, and ankle, which remain relatively constant over the life span. The other nine girths, the changeable ones, were measured at these sites: shoulder, chest, waist, navel, hip, thigh, bicep, forearm, and calf. In addition to the skeletal and girth measurements, recorded in centimeters (cm) is height (cm). Data information stem from such website: http://www.sci.usq.edu.au/staff/dunn/Datasets /applications/biology/body.html

4. Result

...

5. Conclusion

...

6. Appendix

code:

PROC IMPORT OUT= SASUSER.BODY
DATAFILE= "C:\Documents and Settings\Administrator\desktop\Project\body.dat";
DBMS=TAB REPLACE;
GETNAMES=YES;
DATAROW=2;
RUN;

/*----------------------------------------

sifting data: gender=female, age less than 27

-----------------------------------------*/
proc iml;
use sasuser.body ;
read all var {'biacromial' 'pelvic_breadth' 'bitrochanteric' 'chest_depth' 'chest_diam' 'elbow_diam' 'wrist_diam'
'knee_diam' 'ankle_diam' 'shoulder_girth' 'chest_girth' 'waist_girth' 'navel_girth' 'hip_girth' 'thigh_girth' 'bicep_girth' 'forearm_girth' 'knee_girth' 'calf_girth' 'ankle_girth' 'wrist_girth' 'height' 'age' }into x;
read all var {'weight'} into y;
run;

data sasuser.bodysl;
set sasuser.body;
if 0 le age le 27 & gender='1'; run;

/*----------------------------
Normality Test of Weigth
-----------------------------*/

proc univariate data=sasuser.bodysl normal;
var weight;
histogram/normal;
run;

/*---------------------------------
Correlation between variables
----------------------------------*/

proc corr data=sasuser.bodysl;
var biacromial pelvic_breadth bitrochanteric chest_depth chest_diam elbow_diam wrist_diam knee_diam ankle_diam shoulder_girth chest_girth waist_girth navel_girth hip_girth thigh_girth
bicep_girth forearm_girth knee_girth calf_girth ankle_girth wrist_girth height;
run;

data sasuser.body;
set sasuser.bodysl;
keep weight biacromial pelvic_breadth bitrochanteric chest_depth wrist_diam knee_diam ankle_diam chest_girth thigh_girth calf_girth ankle_girth height;
run;

/*----------------------------------
Initial multiple regression Model
-----------------------------------*/
proc iml;
use sasuser.bodysl;
read all var {'biacromial' 'pelvic_breadth' 'bitrochanteric' 'chest_depth' 'wrist_diam' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth' 'calf_girth' 'ankle_girth' 'height' } into x;
read all var{'weight'} into y;
n=nrow(x);
m=ncol(x);
x=j(n,1,1)x;
beta=inv(x`*x)*x`*y;
print beta;
run;

/*-------------------------------------
First round t-test for coefficient
--------------------------------------*/
proc iml;
use sasuser.bodysl;
read all var {'biacromial' 'pelvic_breadth' 'bitrochanteric' 'chest_depth' 'wrist_diam' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth' 'calf_girth' 'ankle_girth' 'height' } into x;
read all var{'weight'} into y;
n=nrow(x);
m=ncol(x);
x=j(n,1,1)x;
beta=inv(x`*x)*x`*y;
print beta;
sse=y`*y-beta`*x`*y;
df_sse=n-m-1;
mse=sse/df_sse;
varbeta=inv(x`*x)*mse;
print varbeta;
do i=2 to 13;
g=varbeta[i,i];
sqr=sqrt(g);
ttest1=beta[i,1]/sqr;
if ttest1<0 p="2*probt(ttest1,89);">0 then p=2*(1-probt(ttest1,89));
print p;
end;
run;

/*------------------------------------------------------------------
P value of variable Pelvic_breadth=0.7289, drop pelvic_breadth
------------------------------------------------------------------*/
proc iml;
use sasuser.bodysl;
read all var {'biacromial' 'bitrochanteric' 'chest_depth' 'wrist_diam' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth' 'calf_girth' 'ankle_girth' 'height' } into x;
read all var{'weight'} into y;
n=nrow(x);
m=ncol(x);
x=j(n,1,1)x;
beta=inv(x`*x)*x`*y;
sse=y`*y-beta`*x`*y;
df_sse=n-m-1;
mse=sse/df_sse;
varbeta=inv(x`*x)*mse;
print varbeta;
do i=2 to 12;
g=varbeta[i,i];
sqr=sqrt(g);
ttest1=beta[i,1]/sqr;
if ttest1<0 p="2*probt(ttest1,90);">0 then p=2*(1-probt(ttest1,90));
print p;
end;
run;

/*-----------------------------------------------------------
P value of variable Wrist_diam=0.49385, drop Wrist_diam
-----------------------------------------------------------*/
proc iml;
use sasuser.bodysl;
read all var {'biacromial' 'bitrochanteric' 'chest_depth' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth'
'calf_girth' 'ankle_girth' 'height' } into x;
read all var{'weight'} into y;
n=nrow(x);
m=ncol(x);
x=j(n,1,1)x;
beta=inv(x`*x)*x`*y;
sse=y`*y-beta`*x`*y;
df_sse=n-m-1;
mse=sse/df_sse;
varbeta=inv(x`*x)*mse;
print varbeta;
do i=2 to 11;
g=varbeta[i,i];
sqr=sqrt(g);
ttest1=beta[i,1]/sqr;
if ttest1<0 p="2*probt(ttest1,91);">0 then p=2*(1-probt(ttest1,91));
print p;
end;
run;

/*------------------------------------------------
P value of variable Height=0.58, drop height
-------------------------------------------------*/
proc iml;
use sasuser.bodysl;
read all var {'biacromial' 'bitrochanteric' 'chest_depth' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth' 'calf_girth' 'ankle_girth'} into x;
read all var{'weight'} into y;
n=nrow(x);
m=ncol(x);
x=j(n,1,1)x;
beta=inv(x`*x)*x`*y;
sse=y`*y-beta`*x`*y;
df_sse=n-m-1;
mse=sse/df_sse;
varbeta=inv(x`*x)*mse;
print varbeta;
do i=2 to 10;
g=varbeta[i,i];
sqr=sqrt(g);
ttest1=beta[i,1]/sqr;
if ttest1<0 p="2*probt(ttest1,92);">0 then p=2*(1-probt(ttest1,92));
print p;
end;
run;

/*-------------------------------------------------------------
P value of variable ankle_girth=0.6952, drop ankle_girth
-------------------------------------------------------------*/
proc iml;
use sasuser.bodysl;
read all var {'biacromial' 'bitrochanteric' 'chest_depth' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth' 'calf_girth' } into x;
read all var{'weight'} into y;
n=nrow(x);
m=ncol(x);
x=j(n,1,1)x;
beta=inv(x`*x)*x`*y;
sse=y`*y-beta`*x`*y;
df_sse=n-m-1;
mse=sse/df_sse;
varbeta=inv(x`*x)*mse;
print varbeta;
do i=2 to 9;
g=varbeta[i,i];
sqr=sqrt(g);
ttest1=beta[i,1]/sqr;
if ttest1<0 p="2*probt(ttest1,93);">0 then p=2*(1-probt(ttest1,93));
print p;
end;
run;
/*----------------------
Confidence Interval
-----------------------*/
proc iml;
use sasuser.bodysl;
read all var{'biacromial' 'bitrochanteric' 'chest_depth' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth'
'calf_girth' } into x;
read all var{'weight'} into y;
t=tinv(0.975,93);
print t;
n=nrow(x);
m=ncol(x);
x=j(n,1,1)x;
beta=inv(x`*x)*x`*y;
sse=y`*y-beta`*x`*y;
df_sse=n-m-1;
mse=sse/df_sse;
varbeta=inv(x`*x)*mse;
upperb=j(9,1);
lowerb=j(9,1);
do i=1 to 9;
g=varbeta[i,i];
sqr=sqrt(g);
upperb[i,1]=beta[i,1]+t*sqr;
lowerb[i,1]=beta[i,1]-t*sqr;
end;
print upperb;
print lowerb;
run;

/*------------------------------
ANOVA Table Using Proc IML
-------------------------------*/
proc iml;
use sasuser.bodysl;
read all var {'biacromial' 'bitrochanteric' 'chest_depth' 'knee_diam' 'ankle_diam' 'chest_girth' 'thigh_girth' 'calf_girth' } into x;
read all var{'weight'} into y;
n=nrow(x);
m=ncol(x);
vector=j(102,8);
do i=1 to 8;
xbar=mean(x[:,i]);
do count=1 to 102;
vector[count,i]=xbar;
end;
end;
print vector;
cenX=j(102,8);
do k=1 to 102;
do q=1 to 8;
cenX[k,q]=x[k,q]-vector[k,q];
end;
end;
print cenX;
ybar=mean(y[:,1]);
print ybar;
cenbeta=inv(cenX`*cenX)*cenX`*y;
ssr=cenbeta`*cenX`*y;
sse=y`*y-n*(ybar*ybar)-cenbeta`*cenX`*y;
sst=y`*y-n*ybar*ybar;
df_sse=n-m-1;
df_ssr=m;
mse=sse/df_sse;
print ssr;
msr=ssr/df_ssr;
f=msr/mse;
print beta;
print sse ssr df_sse df_ssr;
print mse msr;
print f;
pvalue=1-probf(125.008,8,93);
print pvalue;
run;

/*----------------------------
ANOVA Table Using PROC REG
----------------------------*/
proc reg data=sasuser.body ;
model weight=biacromial bitrochanteric chest_depth knee_diam ankle_diam chest_girth thigh_girth calf_girth/clb;
run;

Request for final report, please send email to stefanie.cao@gmail.com with title: ''Request for Human Weight Research Report''.