Page 90 - Basic Statistics

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estimate  . If the model is correct then both are unbiased estimate. In the event
the hypothesis  1 = 0 is true, both the average sum of squares, ie MS (Reg) and

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MS (Res) estimate  . If  1 away from 0 then MS (Reg) increased greater than
MS (Res). An analysis of variance results is quite good if the number of squares

that is explained much greater than the unexplained sum of squares. The ratio

between MS (Reg) to MS (Res) that large indicates  1 is not equal to zero. If the

assumption that the residual normally distributed is valid, and the hypothesis

 1= 0 is true, then the ratio between MS (Reg) to MS (Res) follows the

distribution F.

By using the F distribution approach in testing the significance of a

ˆ
ˆ
ˆ
allegation regression equation Y = β + β Xj, then RSS (Reg) states the portion
j
0
1
of the unexplained component that has been corrected, and SS(Res) states the
portion of unexplained component. This method can also be used to test
hypotheses:

H 0 :  1 = 0. ( R10 )

H 1 :  1  0

Furthermore, the formula for calculating the F statistic is

F = MS(Reg) / MS(Res) ( R11 )

where
MS (Reg) = Mean sum of squares regression

MS (Res) = Mean sum of squares residual

Which can be compared to the critical value , of the F distribution with 1

degrees of freedom in numerator and n-2 degrees of freedom in denominator.

~~* CHAPTER 5 LINEAR REGRESSION MODEL *~~