Page 130 - Basic Statistics

125

2. Data on the measurements results of several organs of the body are presented

in Table 5.18. With linear regression model, want to investigate the influence of
a group of independent variables, namely the size of the lungs (X1), heart (X2),

liver (X3), spleen (X4) against Kidney size (Y). In Table 5.19, through the SAS

output is presented the matrix ( X’X ) of linear regression model.
-1

a. Find the estimated regression equation

b. Test the significance of the regression model by testing the following
formulation of the test hypothesis

H0 : 1 = 2 = 3 = 4 =0

H1 : j  0 , For the smallest one of the j j = 1, 2, 3,4

Find the sum of squares regression using

SS(Reg) = SS( 1  0 ) + SS( 2  0 , 1 )+ SS( 3  0 , 1 , 2 )

+ SS( 4  0 , 1 , 2 , 3 )

c. Perform partial testing for each regression coefficients, i.e test the following

hypotheses.

H0 : j = 0.

H1 : j  0 , j = 1, 2, 3, 4

d. Perform sequential testing on the order of independent variables X1, X2, X3 ,

and X4.

e. By defining a general linear hypothesis, test the contribution 3 regressors,

namely the lungs (X1), liver (X3), and spleen (X4), to the sum of squares

regression, which is testing the hypothesis H0 : 1 = 3 = 4 = 0.

f. By defining a general linear hypothesis, test the hypothesis

H0: 0 = 0 dan 1 = 3 = 4 = 0.

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