You decide to estimate the following quarterly sales forecasting model for new boat sales in your local county:
Qt = a + bt + cD
The equation is estimated using quarterly data on new boat sales in the county from the 3rd quarter of 2001 to the 4th quarter of 2007 (t = 1,...,26). The variable D is a dummy variable for the second quarter, which is the "season" for selling new boats: D = 1 in the second quarter, and 0 otherwise. The results of the estimation are:
|
Dependent Variable
|
LNQ
|
R-SQUARE
|
F-RATIO
|
P-VALUE ON F
|
|
|
OBSERVATIONS
|
64
|
0.8464
|
110.25
|
0.0001
|
|
|
|
|
PARAMETER
|
STANDARD
|
|
|
|
VARIABLE
|
|
ESTIMATE
|
ERROR
|
T-RATIO
|
P-VALUE
|
|
INTERCEPT
|
|
5.65
|
3.20
|
1.77
|
0.0825
|
|
LNP
|
|
-1.02
|
0.59
|
-1.73
|
0.0890
|
|
LNM
|
|
0.45
|
0.22
|
2.05
|
0.0452
|
|
LNPR
|
|
-2.0
|
0.75
|
-2.67
|
0.0098
|
a. Express the estimated demand equation in logarithms.
b. Is X a normal or an inferior good? And how are goods X and R related? Explain.
c. Which of the parameter estimates are statistically significant at the 5 percent level?
d. Estimate the own-price elasticity for good X, the cross-price elasticity for goods X and R, and the income elasticity for good X.
e. Holding all other things constant, if household income were to fall by 22%, what would we expect to happen to quantity demanded? Explain.
f. Holding all other things constant, if own price were to increase by 22%, what would we expect to happen to quantity demanded? Explain.
g. Holding all other things constant, if the price of R were to fall by 8%, what would we expect to happen to quantity demanded? Explain.