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 |
Sales |
|||
|---|---|---|---|---|---|
|
($/Gallon) |
(x 1000 Gal) |
||||
| ii | xixi | yiyi | xixi yiyi | xi2xi2 | yi2yi2 |
| 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 | 130 | 2,210 | 289 | 16,900 |
| 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 | 200 | 2,400 | 144 | 40,000 |
| 10 | 15.5 | 190 | 2,945 | 240.25 | 36,100 |
| Total | 151 | 1,740 | selector 1
|
2,312 | selector 2
|
Points:
|
Regression Parameters |
Estimations |
|---|---|
| Slope (ββ ) | selector 1
|
| Intercept (αα ) | selector 2
|
In words, for a dollar increase in the selling price, the expected sales will selector 1
by selector 2
gallons in a given sales region.
What is the standard error of the estimate (sese )?
15.390
14.049
17.336
What is the estimate of the standard deviation of the estimated slope (sbsb )?
3.069
2.487
2.725
Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0 ) between the variables? (Hint: t0.025,8=2.306t0.025,8=2.306 )
Yes
No
Complete the following worksheet and then use it to calculate the coefficient of determination.
|
ii |
xixi |
yiyi |
yˆy^ |
(yˆi−y¯)2y^i−y¯2 |
(yi−y¯)2yi−y¯2 |
|---|---|---|---|---|---|
| 1 | 15 | 160 | 175.329 | 1.766 | 196.000 |
| 2 | 13.5 | 220 | 195.266 | 452.243 | 2,116.000 |
| 3 | 16.5 | 140 | 155.392 | 346.258 | 1,156.000 |
| 4 | 14.5 | 190 | 181.975 | 63.601 | 256.000 |
| 5 | 17 | 130 | 148.746 | 637.765 | 1,936.000 |
| 6 | 16 | 160 | 162.038 | 143.089 | 196.000 |
| 7 | 13 | 200 | 201.912 | 779.080 | 676.000 |
| 8 | 18 | 150 | 135.455 | 1,485.717 | 576.000 |
| 9 | 12 | 200 | 215.204 | 1,697.770 | 676.000 |
| 10 | 15.5 | 190 | 168.683 | 28.270 | 256.000 |
| Total | selector 1
|
selector 2
|
Points:
The coefficient of determination (r2r2 ) is selector 1
According to the regression model, which of the following is the best estimate together with the 95 percent prediction interval of paint sales (in thousands of gallons) in a sales region where the selling price is $12.50?
208.575 ± 2(17.336)
384.575 ± 2(3.069)
208.575 ± 2(3.069)
384.575 ± 2(17.336)
What is the price elasticity of demand at a selling price of $12.50?
-0.54
-0.05
-0.80
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