Page 92 - Basic Statistics

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Testing this hypothesis using t-student distribution approach. Statistic t is

calculated by

ˆ
t = (β –0) / S ( R15 )
1 ˆ 1 β
where
2
S = MS(Res) /  ( Xj X - )
ˆ
1 β

2
= MS(Res) / (  X − (  X ) 2 / ) n
j j
Where:

t = Statistic value t

ˆ
β = Estimated value for the coefficient of the explanatory variables
1
ˆ
S = Standard deviation of the coefficient β
ˆ
1
1 β
T- statistic follows the t-student distribution and having n-2 degrees of freedom

Criteria testing:

The test requires a two-tailed test and if this test use significance level  ,

then testing criteria as follows:
H0 is accepted if  t-actual   t/2-table , or

Pr = [ P ( t  -t actual ) + P ( t  t actual) ]   , otherwise

( R16 )

H0 is rejected if  t-actual  > t/2-table , or

Pr = [ P ( t  -t actual ) + P ( t  t actual) ] < .

Worked Example 5.1 :

A study was conducted to determine the relationship between the
Increased consumption of gasoline (Y) with the level of car sales (X) in the

Samarinda City. The data given in Table 5.2 were collected over twelve months.

~~* CHAPTER 5 LINEAR REGRESSION MODEL *~~