Question

E-Bags, Inc. sells premium designer backpacks through cable TV infomercials. The head of the company’s marketing department wants to determine the relationship between monthly backpack sales and the number of monthly TV infomercials. The data he gathered and the corresponding regression summary output are shown below.

Sales	TV Ads	SUMMARY OUTPUT
2.6	20	Regression Statistics
2.3	18	Multiple R	0.984
2.9	23	R Square	0.967
2.8	21	Adjusted R Square	0.965
1.5	11	Standard Error	0.145
3.4	25	Observations	15
3.2	22
1.9	15	ANOVA
3.3	24		df	SS	MS	F	F-signif.
2.2	18	Regression	1	8.124	8.124	386.426	0.000
1.6	14	Residual	13	0.273	0.021
2.7	19	Total	14	8.397
3.7	26
3.9	29		Coefficients	Standard Error	t Stat	P-value
3.8	27	Intercept	-0.328	0.163	-2.012	0.065
		TV Ads	0.150	0.008	19.658	0.000

Based on the above information:

1. Interpret the correlation coefficient.

2. Write out the multiple regression model.
3. Interpret the equation’s regression coefficient TV ads.

Answer 1

(a) The correlation coefficient between Sales and TV Ads has come out to be 0.984, which indicates there is a very strong positive relationship between the two variables, that is, as the number of TV Ads increases, the Sales of the product also increases at a linear rate.

(b) Here, y = Sales, x = TV Ads. Hence, .

(c) The regression coefficient of the TV Ads variable is 0.150. This means that if there is an increase in the number of TV Ads by 1, then the Sales of the product will increase 0.150 units.