Question

10 states comparable in size, wealth, and purchasing powers were selected to investigate the effect of marketing expenditures on sales of televisions. For each state, the marketing expenditure X-thousands of dollars and the sales Y-units sold are shown below:

Marketing expenditure	sales
4.9	27
8.8	42
2.1	16
7.6	35
4.4	33
3.5	28
7.0	40
10.1	43
5.6	35
3.0	21

Determine the regression equation for predicting sales from expenditure. Construct the 99 percent confidence interval for the slope of the regression line.

If the prediction equation derived was to be applied to the population as a whole, what proportion of the variability in sales figures could be predicted from knowledge of marketing expenditure.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.919158799
R Square	0.844852898
Adjusted R Square	0.825459511
Standard Error	3.741928104
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	609.9837925	609.9837925	43.56396678	0.000169334
Residual	8	112.0162075	14.00202593
Total	9	722
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	14.07779579	2.961991321	4.752814664	0.001440031	7.247431551
Marketing expenditure	3.144246353	0.476379272	6.600300507	0.000169334	2.045713781

Sales^= 14.0778 + 3.144 * Marketing expenditure

99% confidence interval for slope

1.545809

4.742683

r^2 = 0.8449

hence 84.49 % of variation in sales figures is explained by this model