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 xixiyiyi 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 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 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 1,760 ? 2,312 ? Regression Parameters Estimations Slope (ββ) ? Intercept (αα) ? In words, for a dollar increase in the selling price, the expected sales will (increase?, or decrease?) by ? gallons in a given sales region. What is the standard error of the estimate (sese)? 14.141 17.200 15.491 What is the estimate of the standard deviation of the estimated slope (sbsb)? 2.504 2.743 3.045 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) No Yes 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 15 160 177.649 2.719 256.000 2 13.5 220 202.382 696.010 1,936.000 3 16.5 140 152.915 532.917 1,296.000 4 14.5 190 185.893 97.871 196.000 5 17 120 144.671 981.506 3,136.000 6 16 160 161.160 220.226 256.000 7 13 210 210.627 1,199.029 1,156.000 8 18 150 128.182 2,286.561 676.000 9 12 220 227.116 2,612.845 1,936.000 10 15.5 190 169.404 43.507 196.000 Total ? ? The coefficient of determination (r2r2) is ? 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? 437.605 ± 2(17.200) 218.855 ± 2(17.200) 437.605 ± 2(3.045) 218.855 ± 2(3.045) What is the price elasticity of demand at a selling price of $12.50? -0.58 -0.07 -0.94 -0.06

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 xixiyiyi 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 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 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 1,760 ? 2,312 ? Regression Parameters Estimations Slope (ββ) ? Intercept (αα) ? In words, for a dollar increase in the selling price, the expected sales will (increase?, or decrease?) by ? gallons in a given sales region. What is the standard error of the estimate (sese)? 14.141 17.200 15.491 What is the estimate of the standard deviation of the estimated slope (sbsb)? 2.504 2.743 3.045 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) No Yes 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 15 160 177.649 2.719 256.000 2 13.5 220 202.382 696.010 1,936.000 3 16.5 140 152.915 532.917 1,296.000 4 14.5 190 185.893 97.871 196.000 5 17 120 144.671 981.506 3,136.000 6 16 160 161.160 220.226 256.000 7 13 210 210.627 1,199.029 1,156.000 8 18 150 128.182 2,286.561 676.000 9 12 220 227.116 2,612.845 1,936.000 10 15.5 190 169.404 43.507 196.000 Total ? ? The coefficient of determination (r2r2) is ? 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? 437.605 ± 2(17.200) 218.855 ± 2(17.200) 437.605 ± 2(3.045) 218.855 ± 2(3.045) What is the price elasticity of demand at a selling price of $12.50? -0.58 -0.07 -0.94 -0.06

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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	Sales
($/Gallon)	(x 1000 Gal)
ii	xixi	yiyi	xixiyiyi	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	120	2,040	289	14,400
6	16	160	2,560	256	25,600
7	13	210	2,730	169	44,100
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	1,760	?	2,312	?

Regression Parameters	Estimations
Slope (ββ)	?
Intercept (αα)	?

In words, for a dollar increase in the selling price, the expected sales will (increase?, or decrease?) by ? gallons in a given sales region.

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

14.141

17.200

15.491

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

2.504

2.743

3.045

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

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	177.649	2.719	256.000
2	13.5	220	202.382	696.010	1,936.000
3	16.5	140	152.915	532.917	1,296.000
4	14.5	190	185.893	97.871	196.000
5	17	120	144.671	981.506	3,136.000
6	16	160	161.160	220.226	256.000
7	13	210	210.627	1,199.029	1,156.000
8	18	150	128.182	2,286.561	676.000
9	12	220	227.116	2,612.845	1,936.000
10	15.5	190	169.404	43.507	196.000
			Total	?	?

The coefficient of determination (r2r2) is ?

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?

437.605 ± 2(17.200)

218.855 ± 2(17.200)

437.605 ± 2(3.045)

218.855 ± 2(3.045)

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

-0.58

-0.07

-0.94

-0.06

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