ADJUSTED REGRESSION MODEL
6. Adjusted regression model:
From the beginning, our model has 6 independent variables which are
Price(X
1
), Income(X
2
), Prime(X
3
), Unemployment(X
4
), Stock(X
5
), Population(X
6
).
However, after finishing test hypothesis relating to regression a coefficient, we
decide to reject 2 independent variables: Unemployment(X
4
) and Stock(X
5
) that
have no meaning in the model and keep 4 others.
Conclusion: We have the adjusted OLS regression:
Figure 6.2: The estimate OLS regression (Source: Gretl)
The estimated OLS regression is:
= 24761.6 + 47.6529Price + 903.472Income - 41.6461Prime - 153.443Pop.
With: QNC : Quantity of new cars sold quarterly (1000 units)
Price: Average real price index of a new car ( $)
Income: Per capita disposable personal income (1000$)
Prime: Prime interest rate (%)
Pop: Population (1000 people)
It can be shown from the figure 6.2 that:
Meaning of coefficient:
-
Intercept= 24761.6 : If all these other factors equal to zero, quantity of new
cars sold quarterly equals to 24761.6 x10
3
units . But this situation cannot occur
due to the theory because the quantity of good sold in the market always depends
other factors that affect to demand and supply.
-
Coefficient of Price = 47.6529. If the real price index of a new car increases
1$ , the quantity of new cars sold quarterly will increase 47.6529x10
3
units.
⇒ It follows the law of macroeconomics mentioned in theory background above.
-
Coefficient of Income= 903.472. If the capita disposable personal income
increases 1$, the quantity of new cars quarterly sold will increase 903.472 units.
⇒ It follows the law of microeconomics mentioned in theory background above .
-
Coefficient of Prime= - 41.6461. If the prime rate increases 1%, the quantity
of new cars sold quarterly will decrease 41.6461x10
3
units.
⇒ It follows the law of macroeconomics mentioned in theory background above .
-
Coefficient of Population= -153.443. If the population increases 1
people, the quantity of new cars sold quarterly will decrease 153.443 units.
⇒ It doesn`t follow the law of economics. And, now, there is no theory to explain
about that.
R
2
= 0.483821. It means that the 4 regressors explain 48.38% of the variance
of Quantity of new cars sold quarterly. It is quite similar to model 1.
SER = 247.1650. It estimates standard deviation of error u
i
. A relatively high
spread of scatter plot means that prediction of Quantity of new cars sold
quarterly base on these variables might be not much reliable. It is quite
similar to model 1.
All the independent variables show *** with the statistical significance of
1%.
P-value(F)= 5.15e
-08
< 0.05
Model 2 has the statistical significance
VII. Robustness check