You are the manager of a firm that sells a leading brand of

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

Solution

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