Ten sales regions of equal sales potential for a company wer

Ten sales regions of equal sales potential for a company were randomly selected. The advertising expenditures (in units of $10,000) in these 10 sales regions were purposely set during July of last year at, respectively, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14. The sales volumes (in units of $10,000) were then recorded for the 10 sales regions and found to be, respectively, 101, 86, 85, 98, 121, 89, 126, 120, 90, and 86. Assuming that the simple linear regression model is appropriate, it can be shown that b0 = 93.2909, b1 = .7273. Find a 95 percent confidence interval for the slope 1 of the simple linear regression model describing the sales volume data

Solution

Ten sales regions of equal sales potential for a company were randomly selected. The advertising expenditures (in units of $10,000) in these 10 sales regions were purposely set during July of last year at, respectively, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14. The sales volumes (in units of $10,000) were then recorded for the 10 sales regions and found to be, respectively, 101, 86, 85, 98, 121, 89, 126, 120, 90, and 86. Assuming that the simple linear regression model is appropriate, it can be shown that b0 = 93.2909, b1 = .7273. Find a 95 percent confidence interval for the slope 1 of the simple linear regression model describing the sales volume data

Regression Analysis

r²

0.018

n

10

r

0.136

k

1

Std. Error

17.015

Dep. Var.

sales

ANOVA table

Source

SS

df

MS

F

p-value

Regression

43.6364

1  

43.6364

0.15

.7080

Residual

2,315.9636

8  

289.4955

Total

2,359.6000

9  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=8)

p-value

95% lower

95% upper

Intercept

93.2909

18.5914

5.018

.0010

50.4191

136.1627

Expenditure

0.7273

1.8732

0.388

.7080

-3.5924

5.0470

95% CI for slope 1 = (-3.5924, 5.0470)

Regression Analysis
	r²	0.018	n	10
	r	0.136	k	1
	Std. Error	17.015	Dep. Var.	sales
ANOVA table
Source	SS	df	MS	F	p-value
Regression	43.6364	1	43.6364	0.15	.7080
Residual	2,315.9636	8	289.4955
Total	2,359.6000	9
Regression output				confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	93.2909	18.5914	5.018	.0010	50.4191	136.1627
Expenditure	0.7273	1.8732	0.388	.7080	-3.5924	5.0470