You are the manager of a firm that sells a leading brand of alkaline batteries.
ID: 3383587 • Letter: Y
Question
You are the manager of a firm that sells a leading brand of alkaline batteries. You hire a consultant to find a demand function for your alkaline batteries. You give the consultant annual data on the quantity sold, price and the average income of consumers in various regions around the world where the batteries are sold. The consultant sends you back a file with a LOG-LINEAR regression with the following results:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.97
R Square
0.94
Adjusted R Square
0.94
Standard Error
0
Observations
49
ANOVA
df
SS
MS
F
Significance F
Regression
2
0.00702
0.004
370.08
0.00
Residual
46
0.00044
0.0000
Total
48
.--745
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1.29
0.41
3.12
0.00
0.46
2.12
ln (Price)
-0.07
0
-26.62
0.00
-0.08
-0.07
ln (Income)
-0.03
0.09
-0.33
0.74
-0.22
0.16
Which regression coefficients are significant at the 5% level? Why?
Determine the likely impact of a 3% decline in global income on the overall demand for your product.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.97
R Square
0.94
Adjusted R Square
0.94
Standard Error
0
Observations
49
ANOVA
df
SS
MS
F
Significance F
Regression
2
0.00702
0.004
370.08
0.00
Residual
46
0.00044
0.0000
Total
48
.--745
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1.29
0.41
3.12
0.00
0.46
2.12
ln (Price)
-0.07
0
-26.62
0.00
-0.08
-0.07
ln (Income)
-0.03
0.09
-0.33
0.74
-0.22
0.16
Explanation / Answer
1the coefficient for which the p value is >0.5 is said to be significant. hence income is significant.
the regression equation is
Ln(y)=ln(1.29-0.03*income)
when income 3%income,
LN(y)=LN(1.29-0.03*3)=0.1823
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