Kalamazoo Brewing Company (KBC) currently sells its microbrews only in Michigan.
ID: 1193650 • Letter: K
Question
Kalamazoo Brewing Company (KBC) currently sells its microbrews only in Michigan. The company’s Marketing department has collected data from its distributors. This data is the quantity and price (per case) of its microbrews as well as the average income of consumers living in Michigan. Using a linear demand specification, an economic consultant has obtained the following results from the least squares estimates of demand for microbrews:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.29
R Square
0.09
Adjusted R Square
0.05
Standard Error
151.15
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
2
100,540.93
50,270.47
2.20
0.12
Residual
47
1,073,835.44
22,847.56
Total
49
1,174,376.00
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-42.65
496.56
-0.09
0.93
-1041.60
956.29
Price
2.62
13.99
0.19
0.85
-25.53
30.76
Income
14.32
6.83
2.10
0.04
,58
28.05
Provide an economic interpretation of the results.
How are quantity and price related?
How is income related to quantity?
Are the factors affecting the quantity demanded of microbrews statistically significant?
What is the value of R squared? What can you infer from this value of R-squared?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.29
R Square
0.09
Adjusted R Square
0.05
Standard Error
151.15
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
2
100,540.93
50,270.47
2.20
0.12
Residual
47
1,073,835.44
22,847.56
Total
49
1,174,376.00
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-42.65
496.56
-0.09
0.93
-1041.60
956.29
Price
2.62
13.99
0.19
0.85
-25.53
30.76
Income
14.32
6.83
2.10
0.04
,58
28.05
Explanation / Answer
(a) From the regression output summary we can infer that, the linear demand curve is:
Quantity, Q = - 42.65 + 2.62P (Price) + 14.32M (Income)
(b) Quantity is positively related to price. As price increases (decreases), quantity increases (decreases) which is indicated by the positive slope-coefficient of the Price variable.
(c) Quantity is positively related to income. As income increases (decreases), quantity increases (decreases) which is indicated by the positive slope-coefficient of the Income variable. This indicates an inferior good.
(d) If we assume a 5% level of significance, a variable is statistically significant if its P-value is lower than 0.05. For Price, p-value is higher than 0.05 but for income, p-value is 0.04 < 0.05. Therefore, income is statistically significant but price is not.
(e) R2 = 0.09. This indicates that the regression model is explained by the data only to the extent of 9%, which is too low indicating a poor goodness of fit.
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