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 RegionSelling PriceSales ($/Gallon)(x 1000 Gal)iixixiyiyixixiyiyixi2xi2yi2yi21151602,40022525,600213.52202,970182.2548,400316.51402,310272.2519,600414.51902,755210.2536,1005171202,04028914,4006161602,56025625,6007132102,73016944,1008181502,70032422,5009122102,52014444,1001015.51902,945240.2536,100Total1511,750 2,312 What is the estimate of the standard deviation of the estimated slope (sbsb)?2.627 3.173 2.877 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

For the given data the regression output, as obtained in excel, is as follows Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 409.3103 48.24282345 8.484378 2.85E-05 298.0622 520.5585 Selling price -15.5172 3.172771549 -4.89075 0.001208 -22.8337 -8.20082 From the above output, it can be obtained that the slope value is given by the coefficient of the "Selling price" which is -15.5172. The value of the required standard deviation is given by the corresponding value of standard error in the output which is 3.173.It can be observed from the output that the test statistic value (t Stat) for the slope is -4.89 and the critical values are -2.306 and 2.306. Since the test statistic is less than the critical value -2.306, we have sufficient evidence to reject the hypothesis that there is no significant relationship between sales and price. So the correct answer is Yes.

Answered: Suppose the Sherwin-Williams Company is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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	210	2,520	144	44,100
10	15.5	190	2,945	240.25	36,100
Total	151	1,750		2,312

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

2.627

3.173

2.877

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