Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price ($/Gallon) Sales (x 1000 Gal) i 2 Zi Yi Zith 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 140 2,380 289 19,600 6 16 160 2,560 256 25,600 7 13 200 2,600 169 40,000 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,770 2,312 Regression Parameters Estimations Slope (B) Intercept (a) In words, for a dollar increase in the selling price, the expected sales will What is the standard error of the estimate (&)? O 14.889 12.180 13.342 gallons in a given sales region. What is the estimate of the standard deviation of the estimated slope (86)? O 2.636 2.157 2.362 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., B=0) between the variables? (Hint: to.025,8 = 2.306) ○ No Yes

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter4: Estimating Demand
Section: Chapter Questions
Problem 1E
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Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and
selling price (P) as the independent variable.
Complete the following worksheet and then use it to determine the estimated regression line.
Sales Region
Selling Price
($/Gallon)
Sales
(x 1000 Gal)
i
2
Zi
Yi
Zith
1
15
160
2,400
225
25,600
2
13.5
220
2,970
182.25
48,400
3
16.5
140
2,310
272.25
19,600
4
14.5
190
2,755
210.25
36,100
5
17
140
2,380
289
19,600
6
16
160
2,560
256
25,600
7
13
200
2,600
169
40,000
8
18
150
2,700
324
22,500
9
12
220
2,640
144
48,400
10
15.5
190
2,945
240.25
36,100
Total
151
1,770
2,312
Regression Parameters Estimations
Slope (B)
Intercept (a)
In words, for a dollar increase in the selling price, the expected sales will
What is the standard error of the estimate (&)?
O 14.889
12.180
13.342
gallons in a given sales region.
What is the estimate of the standard deviation of the estimated slope (86)?
O 2.636
2.157
2.362
Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., B=0) between the variables? (Hint:
to.025,8 = 2.306)
○ No
Yes
Transcribed Image Text:Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price ($/Gallon) Sales (x 1000 Gal) i 2 Zi Yi Zith 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 140 2,380 289 19,600 6 16 160 2,560 256 25,600 7 13 200 2,600 169 40,000 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,770 2,312 Regression Parameters Estimations Slope (B) Intercept (a) In words, for a dollar increase in the selling price, the expected sales will What is the standard error of the estimate (&)? O 14.889 12.180 13.342 gallons in a given sales region. What is the estimate of the standard deviation of the estimated slope (86)? O 2.636 2.157 2.362 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., B=0) between the variables? (Hint: to.025,8 = 2.306) ○ No Yes
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