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

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.

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., =0=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	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

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