Page 132 - Basic Statistics

127

-1
Table 5.19 Output SAS for the matrix ( X’X )

X'X Inverse

INTERCEP X1 X2

INTERCEP 0.2143847334 -0.168027136 -0.095712472
X1 -0.168027136 0.6152818699 -0.225741783
X2 -0.095712472 -0.225741783 0.3972158583
X3 0.006655296 -0.015950671 -0.011878562
X4 -0.094818419 -0.038820519 -0.428510383

X3 X4

INTERCEP 0.006655296 -0.094818419
X1 -0.015950671 -0.038820519
X2 -0.011878562 -0.428510383
X3 0.005261954 -0.131875573
X4 -0.131875573 12.971992938

3. The data in Table 5.19 consisted of 26 subjects were selected to study the effect

of exercise activities (running and weight lifting), and body weight on HDL

cholesterol. The subjects consisted of 8 people placed as the control group, 8
people in a group that took part in a relatively rigorous running program, and

10 peopole were placed in a program involving rigorous running and

weightlifting. The weights and HDL cholesterol of the subjects were recorded

after ten weeks of the program. If the linear regression model applied to each

group, there will be three simple linear regression equation. Perform regression
testing of the three equation, through test equality of coefficients (slope).

As a result, the three following models are postulated.

Y j = 01 + 1.1 X1 j +  j j = 1, 2, . . . 8 (Control group)

Y j = 02+ 1.2 X1 j +  j j = 9, 10, . . . 16 (Running group)

Y j = 03 + 1.3 X1 j +  j j = 17, 18, . . . 26 (Running and lifting group)
If the regression models and composition of data is designed with the X matrix

and the  vector like as Eq.(G.33):

a. Estimate of each regression coefficients

b. Tests equality of the thee slopes through tensting the general linear

hypothesis

~~* CHAPTER 5 THE MULTIPLE LINEAR REGRESSION MODEL *~~