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If H0 is true, then the ratio between the mean of SS(Reg) with mean of SS(Res)

will has F distribution with degrees of freedom of numerator is p, and the
degrees of freedom of denominator is np-1 (proof can be found in Searle, 1971,

and Kshirsagar, 1983). So that the statistic used to test the above hypothesis is

SS ( Reg / ) p
F = (G.20)
SS (Re s / ) n − ( + ) 1
p

Testing criteria:

To a certain significance level  testing used, H0 is accepted if

Fvalue < F (, p, n-p-1) or P( F > Factual ) >  , otherwise H0 is rejected.

Worked Example 5.4:

An expriment was conducted in order to study the zise of squid eaten by

tuna. The regressor variables are characteristics of beak or mouth of the squid.

The regressor variables and response considered for the study are: (X1) Rostral
length in inches, (X2) Wing length in inches, (X3) Rostral to notch length, (X4)

Notch to wing length, (X5) Width in inches, and (Y) weight in pounds. The

study involved measurements and weight taken 22 specimen. The data are

shown in Table 5.9. The model is given by

Y j = 0 + 1X1 j + 2 X2 j +3X3 j + 4 X4 j + 5 X5 j +  j

Test the significance of the regression model.

Worked Solution:
To test the significance of the regression model, formulated the following
hypothesis test.

H0 : 1 = 2 = 3 = 4 = 5 = 0

H1 : j  0 , For the smallest one of the j. j = 1, 2, 3, 4, 5.

SS ( Reg / ) p 41 . 602
In Table 5.10 , given the statistic F = = = 84 . 070
p
SS (Re s / ) n − ( + ) 1 . 0 4948

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