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Significance of Parameters
and
Overall Significance of Regression
TEST
OF SIGNIFICANCE OF PARAMETER ESTIMATES
In order to test the significance of parameter estimates we apply the
t-statistic, where we follow the same procedure as we employed in the
simple regression model.
TEST
OF THE OVERALL SIGNIFICANCE OF THE REGRESSION
The overall significance of the regression can be tested with the ratio of
the explained to the unexplained variance. This follows an F distribution
with k-1 and n-k degrees of freedom, where n is number of observations and
k is number of parameters estimated:
If
the calculated F ratio exceeds the tabular value of F at the specified
level of significance and degrees of freedom, the hypothesis is accepted
that the regression parameters are not all equal to zero and that R2
is significantly different from zero. A "high" value for F
statistic suggests a significant relationship between the dependent and
independent, leading to the rejection of the null hypothesis that the
coefficients of all explanatory variables are jointly zero.
In
order to test the overall significance of the regression we firstly state
the null and the alternative hypothesis. Thus, we set:
H0: b1=b2=.........=bk=0
H1:
not all bi's are 0
EXAMPLE
The calculated F ratio or statistic for the case of a simple regression
and for a regression with n=15, k=3 (ie a multiple regression), we get:
where
the subscripts of F denote the number of degrees of freedom in the
numerator and denominator, respectively. In this simple regression case,
F1, n-2= t2n-2 for the same level
of significance. For a multiple regression with n= 15 and k=13,
.
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© 2002
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Evgenia Vogiatzi <<Previous Next>>
