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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

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
  • 25,850
  • 23,450
  • 23,250
2,312 selector 2
  • 310,800
  • 287,700
  • 264,600

Points:

Regression Parameters

Estimations

Slope ( ) selector 1
  • 2.13
  • 0.79
  • -13.29
Intercept ( ) selector 2
  • 141.84
  • 162.07
  • 374.70

Points:

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Explanation:

In words, for a dollar increase in the selling price, the expected sales will selector 1
  • decrease
  • increase
by selector 2
  • 13,290
  • 790
  • 2,130
gallons in a given sales region.

Points:

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Explanation:

What is the standard error of the estimate (sese )?

15.390

14.049

17.336

Points:

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Explanation:

What is the estimate of the standard deviation of the estimated slope (sbsb )?

3.069

2.487

2.725

Points:

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Explanation:

Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., =0=0 ) between the variables? (Hint: t0.025,8=2.306t0.025,8=2.306 )

Yes

No

Points:

Close Explanation

Explanation:

Complete the following worksheet and then use it to calculate the coefficient of determination.

ii

xixi

yiyi

yy^

(yiy)2y^iy2

(yiy)2yiy2

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
  • 4,149.842
  • 5,635.559
  • 5,663.829
selector 2
  • 10,156.000
  • 5,924.000
  • 8,040.000

Points:

The coefficient of determination (r2r2 ) is selector 1
  • 0.555
  • 0.704
  • 0.701

Points:

Close Explanation

Explanation:

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)

Points:

Close Explanation

Explanation:

What is the price elasticity of demand at a selling price of $12.50?

-0.54

-0.05

-0.80

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