F=25.6
Since the value of the F-statistic exceeds the critical F-value of 2.71 (5%) with k-l=5-l=4 and n-k=33-
5=28 df, we accept the hypothesis that the regression explains a significant proportion of the variation in
per capita personal consumption expenditures (Q) at the 5 percent level of significance. In other words,
we can use F-test to see whether overall estimated equation is significant or not. Also, there is evidence
that at least one independent variable affects
per capita personal consumption expenditures.
c)
Since all of the estimated slope coefficients are statistically significant at better than the 1 percent level,
multicollinearity does not seem to be a problem. Finally, since the value of the D-W statistic falls within
the level of dL and dU, the test for evidence of autocorrelation is indeterminate. Broadly, since n=33,
k=5 and estimated is DW=1.129, we need to find tabular values for critical level of dL=1.127 and
dU=1.813 so evidence of autocorrelation is inconclusive (see the DW scale below).
12

d)
Serial Correlation:
H
o
:
=0 (non-existence of (autocorrelation)
H
1
:
0 (existence of autocorrelation)
Since CHI-SQ (1)=0.051656<
X
2
=3.841, we accept H
o
that estimate regression does not have first order
serial correlation or autocorrelation.
Functional Form:
H
o
:
=0 (non-existence misspecification)
H
1
:
0 (existence misspecification)
The estimated LM version of CHI-SQ is 0.0568721 and with
= 0.05 the tabular value is
X
2
=3.841.
Because CHI-SQ (1)=0.0568721<
X
2
=3.841, then we accept the null hypothesis that there is no
misspecification.
Normality:
H
o
:u
t
=0 (residuals are normally distributed)
H
1
:u
t
0(residuals are not
normally distributed)
Our estimated result of LM version for normality is CHI-SQ(2)=1.28191, and the tabular value with 2
restrictions with
= 0.05 is
X
2
=5.991.
13

Since CHI-SQ(2)=1.28191<
X
2
=5.991, the test result shows that the null hypothesis of normality of the
residuals is accepted.
Heteroscedasticity:
H
o
:
yt
2
=
2
(homoscedasticity)
H
1
:
yt
2
2
(heteroscedasticity)
LM version of our result for the heteroscedasticity is
CHI-SQ(1)=1.00651 and table critical value with 1 restriction with
= 0.05 is
X
2
=3.841. Since CHI-
SQ(1)=1.00651<
X
2
=3.841, we accept the null hypothesis that error term is constant for all the
independent variables.
14

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- Winter '17
- Reay