You hire an economic consultant who comes up with a linear demand specification
ID: 1193630 • Letter: Y
Question
You hire an economic consultant who comes up with a linear demand specification to estimate the demand for your product. He/She sends you the following results:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.62
R Square
0.39
Adjusted R Square
0.37
Standard Error
190.9
Observations
100
ANOVA
df
SS
MS
F
Significance F
Regression
2
2223017.77
1111508.88
3,050.00
0
Residual
97
3535019.49
36443.5
Total
99
5758037.26
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-187.15
534.7
0.35
0.73
-88.56
1254.26
Price
-4.32
0.69
6.26
0
-5.69
-2.96
Income
0.09
0.02
4.47
0
0.05
0.014
Based on these estimates, write an equation that summarizes the demand for your firm’s product.
Holding everything else constant, a $1 increase in the price of the product will affect quantity demanded by how much?
Which regression coefficients are significant at the 5% level? Why?
Comment on how well the regression line fits the data.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.62
R Square
0.39
Adjusted R Square
0.37
Standard Error
190.9
Observations
100
ANOVA
df
SS
MS
F
Significance F
Regression
2
2223017.77
1111508.88
3,050.00
0
Residual
97
3535019.49
36443.5
Total
99
5758037.26
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-187.15
534.7
0.35
0.73
-88.56
1254.26
Price
-4.32
0.69
6.26
0
-5.69
-2.96
Income
0.09
0.02
4.47
0
0.05
0.014
Explanation / Answer
(a) Linear demand equation:
Q = - 187.15 - 4.32P + 0.09M [P: Price & M: Income]
(b) dQ / dP = - 4.32
So, for every $1 increase in P, quantity decreases by $4.32.
(c) A regression coefficient is significant at 5% level if its p-value < 0.05.
So, both price & income are statistically significant since their p-value = 0 each.
(d) R2 is a measure of goodness of fit. The higher the R2, the better the fit and for perfect fit, R2 = 1.
Here, R2 = 0.39 indicating the model is a medium fit.
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