Ten sales regions of equal sales potential for a company were randomly selected.
ID: 3393831 • Letter: T
Question
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
Explanation / Answer
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
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