Enabling Assessment - Demand Estimation and Forecasting Given: The ATV Company produces a specialty cement used in the construction of roads. ATV is a price-setting firm and estimates the demand for its cement using a demand function in the linear form: Q = f (P, M, PR) where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard. The manager of ATV obtained the following results in her attempt to estimate the demand for cement in the succeeding months. The results are presented below: DEPENDENT VARIABLE Qc R- SQUARE F-RATIO P-VALUE ON F OBSERVATIONS 64 0.8093 84.872 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 At the 5% level of significance, which variables are statistically significant? If the price of cement per yard increases by 10, what will happen to the estimated quantity of cement demanded? If tax revenue per capita (M) increases by 10, what will happen to the estimated quantity of cement demanded? If the price of asphalt (PR) decreases by 15, what will happen to the estimated quantity of cement demanded? Explain the value of the coefficient of determination and the overall significance of the model. Calculate the price elasticity, cross-price elasticity, and income elasticity of demand for cement. Explain these figures. Write the resulting regression equation.
Enabling Assessment -
Given: The ATV Company produces a specialty cement used in the construction of roads. ATV is a
Q = f (P, M, PR)
where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard. The manager of ATV obtained the following results in her attempt to estimate the demand for cement in the succeeding months. The results are presented below:
|
DEPENDENT VARIABLE |
Qc |
R- SQUARE |
F-RATIO |
P-VALUE ON F |
|
|
OBSERVATIONS |
64 |
0.8093 |
84.872 |
0.0001 |
|
|
VARIABLE |
PARAMETER ESTIMATE |
STANDARD ERROR |
T-RATIO |
P-VALUE |
|
|
INTERCEPT |
|
8.20 |
4.01 |
2.04 |
0.0461 |
|
PC |
-3.54 |
1.64 |
-2.16 |
0.0357 |
|
|
M |
|
0.64287 |
0.19 |
3.38 |
0.0014 |
|
PA |
0.7854 |
0.38 |
2.07 |
0.0439 |
- At the 5% level of significance, which variables are statistically significant?
-
If the price of cement per yard increases by 10, what will happen to the estimated quantity of cement demanded?
-
If tax revenue per capita (M) increases by 10, what will happen to the estimated quantity of cement demanded?
-
If the price of asphalt (PR) decreases by 15, what will happen to the estimated quantity of cement demanded?
-
Explain the value of the coefficient of determination and the overall significance of the model.
-
Calculate the price elasticity, cross-price elasticity, and income
elasticity of demand for cement. Explain these figures. -
Write the resulting regression equation.
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