Question

You are the manager of a firm that sells a leading brand of alkaline batteries. Click on the link below to access data on the demand for your product. Specifically, the file contains data on the natural logarithm of your quantity sold, price, and the average income of consumers in various regions around the world.

Use the information provided in the excel spreadsheet to perform a log-linear regression.

Excel Data File

Fill in your estimates below:

Instruction: Enter a negative number if the coefficient estimate is negative, and round your response to two decimal places.

lnQ = +   lnP + lnM

Determine the likely impact of a 3 percent decline in global income on the overall demand of your product.

• Demand will decline by approximately 3%, but since income elasticity isn't significantly different from zero, it likely won't fall at all.

• Demand will decline by approximately 0.1%, but since income elasticity isn't significantly different from zero, it likely won't fall at all.

• Demand will fall by nearly 1%, and income elasticity is significantly less than zero.

• Demand will fall by nearly 10%, and income elasticity is significantly less than zero.

LN Quantity	LN Price	LN Income
1.07	1.15	4.4
1.07	1.09	4.39
1.08	0.97	4.4
1.08	1.04	4.39
1.09	0.92	4.39
1.08	0.96	4.39
1.1	0.77	4.39
1.1	0.79	4.39
1.08	1.06	4.39
1.07	1.13	4.39
1.08	0.96	4.4
1.08	1.02	4.39
1.09	0.82	4.39
1.07	1.1	4.39
1.09	0.9	4.39
1.1	0.77	4.39
1.09	0.91	4.4
1.08	1.07	4.4
1.09	0.88	4.39
1.07	1.16	4.39
1.08	1.08	4.4
1.08	1	4.39
1.09	0.88	4.39
1.07	1.13	4.4
1.07	1.09	4.39
1.11	0.64	4.39
1.09	0.9	4.39
1.07	1.19	4.4
1.06	1.27	4.39
1.08	0.94	4.39
1.07	1.1	4.4
1.13	0.28	4.39
1.08	0.97	4.4
1.09	0.86	4.4
1.07	1.13	4.39
1.08	1.03	4.39
1.08	0.96	4.39
1.08	0.95	4.4
1.07	1.12	4.4
1.1	0.7	4.4
1.08	0.99	4.39
1.08	0.98	4.39
1.08	1.07	4.4
1.07	1.1	4.4
1.07	1.21	4.39
1.09	0.93	4.39
1.08	1.04	4.4
1.09	0.9	4.39
1.08	0.97	4.39

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.97
R Square	0.94
Adjusted R Square	0.94
Standard Error	0.00
Observations	49
ANOVA
	df	SS	MS	F	Significance F
Regression	2	0.007017	0.003509	370.382253	0.000000
Residual	46	0.000436	0.000009
Total	48	0.007453
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.29	0.41	3.12	0.00	0.46	2.12	0.46	2.12
LN Price	-0.07	0.00	-26.62	0.00	-0.08	-0.07	-0.08	-0.07
LN Income	-0.03	0.09	-0.33	0.74	-0.22	0.16	-0.22	0.16

Since this is a log-linear demand equation, the best estimate of the income elasticity of demand for your product is -.03. Your batteries are an inferior good. However, note the estimated income elasticity is very close to zero. the estimated income elasticity is not statistically different from zero (the 95 percent confidence interval ranges from a low of -.22 to a high of .16, with a t-statistic that is well below 2 in absolute value). On balance, this means that a 3 percent decline in global incomes is unlikely to impact the sales of your product.

correct answer is (B) Demand will decline by approximately 0.1%, but since income elasticity isn't significantly different from zero, it likely won't fall at all.