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 i 1 2 3 4 5 6 7 8 9 10 Total Selling Price ($/Gallon) Ii 15 13.5 16.5 14.5 17 16 13 18 12 15.5 151 Regression Parameters Slope (8) Intercept (a) Sales (x 1000 Gal) Yi 160 220 140 190 120 160 200 150 210 190 1,740 Estimations Tiyi 2,400 2,970 2,310 2,755 2,040 2,560 2,600 2,700 2,520 2,945 25,800 225 182.25 272.25 210.25 2 In words, for a dollar increase in the selling price, the expected sales will 25,600 48,400 19,600 36,100 14,400 25,600 40,000 289 256 169 324 144 240.25 2,312 286,800 22,500 44,100 36,100 by gallons in a given sales region.

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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
i
1
2
3
4
5
6
7
8
9
10
Total
Selling Price
($/Gallon)
I;
15
13.5
16.5
14.5
17
16
13
18
12
15.5
151
Regression Parameters
Slope (B)
Intercept (a)
Sales
(x 1000 Gal)
Yi
160
220
140
190
120
160
200
150
210
190
1,740
Estimations
TiYi
2,400
2,970
2,310
2,755
2,040
2,560
2,600
2,700
2,520
2,945
25,800 ▼
x ₂²
225
182.25
272.25
210.25
289
256
169
324
144
240.25
2,312
In words, for a dollar increase in the selling price, the expected sales will
Yi²
25,600
48,400
19,600
36,100
14,400
25,600
40,000
22,500
44,100
36,100
286,800 ▼
by
gallons in a given sales region.
Transcribed Image Text:Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region i 1 2 3 4 5 6 7 8 9 10 Total Selling Price ($/Gallon) I; 15 13.5 16.5 14.5 17 16 13 18 12 15.5 151 Regression Parameters Slope (B) Intercept (a) Sales (x 1000 Gal) Yi 160 220 140 190 120 160 200 150 210 190 1,740 Estimations TiYi 2,400 2,970 2,310 2,755 2,040 2,560 2,600 2,700 2,520 2,945 25,800 ▼ x ₂² 225 182.25 272.25 210.25 289 256 169 324 144 240.25 2,312 In words, for a dollar increase in the selling price, the expected sales will Yi² 25,600 48,400 19,600 36,100 14,400 25,600 40,000 22,500 44,100 36,100 286,800 ▼ by gallons in a given sales region.
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