1. Exercise 4.1 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 Ine. Sales Reglen Sales (x1000 Gal) 160 225 Selling Price (s/Gallon) 24 15 13.5 16,5 14.5 17 2 3 220 140 190 4 2.400 2,970 2,310 2,755 2,210 2,560 2.730 182.25 272.25 210.25 289 256 5 130 6 16 13 160 210 25,600 48,400 19,600 36,100 16,900 25,600 44,100 22.500 40,000 36,100 7 169 B 18 150 2.700 324 9 12 200 10 15.5 190 2,400 2,945 25.080 240,25 Total 151 1,750 2,312 14,900 Estimations Regression Parameters Slope() Intercept (a) -13.95 385.64 In words, for a dollar increase in the selling price, the expected sales will by > gallons in a given sales region. What is the standard error of the estimate (8.)? O 14.292 O 15.656 17.473 What is the estimate of the standard deviation of the estimated slope (su)? O 3.094 O 2.530 0 2.772 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (1.e., B = 0) between the variables? (Hint: to .. 2.306) Yes O No Complete the following worksheet and then use it to calculate the coefficient of determination. i 2, y 0.- 1.946 1 15 160 176.395 2 13.5 220 197.320 225.000 2,025.000 1,225.000 3 16.5 140 155.470 4 14.5 190 130 225.000 498.182 381.421 70.057 702.515 157.628 183.370 148.495 5 17 16 160 162.445 6 7 13 210 B 2,025.000 225.000 1,225.000 625.000 625.000 225.000 18 204.295 134.545 218.245 169.420 150 858.197 1,636.607 1,870.130 9 12 200 10 15.5 190 31.136 Total The coefficient of determination (r) 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 gations) in a sales region where the selling price is $12.50? O 396,140 4 2(17.473) O 396.140 A 203.094) O 211.265 A 203.094) 0 211.265 2(17.473) 9 12 200 625.000 218.245 169.420 1,870.130 31.136 10 15.5 190 225.000 Total The coefficient of determination (r) 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 $12.507 O 396.140 + 2(17.473) O 396.140 +243.094) 0 211.265 + 2(3.094) O 211.265 + 2(17.473) What is the price elasticity of demand at a selling price of $12.50? -0.06 -0.05 0 -0.55 0 -0.83 1. Exercise 4.1 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 Ine. Sales Reglen Sales (x1000 Gal) 160 225 Selling Price (s/Gallon) 24 15 13.5 16,5 14.5 17 2 3 220 140 190 4 2.400 2,970 2,310 2,755 2,210 2,560 2.730 182.25 272.25 210.25 289 256 5 130 6 16 13 160 210 25,600 48,400 19,600 36,100 16,900 25,600 44,100 22.500 40,000 36,100 7 169 B 18 150 2.700 324 9 12 200 10 15.5 190 2,400 2,945 25.080 240,25 Total 151 1,750 2,312 14,900 Estimations Regression Parameters Slope() Intercept (a) -13.95 385.64 In words, for a dollar increase in the selling price, the expected sales will by > gallons in a given sales region. What is the standard error of the estimate (8.)? O 14.292 O 15.656 17.473 What is the estimate of the standard deviation of the estimated slope (su)? O 3.094 O 2.530 0 2.772 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (1.e., B = 0) between the variables? (Hint: to .. 2.306) Yes O No Complete the following worksheet and then use it to calculate the coefficient of determination. i 2, y 0.- 1.946 1 15 160 176.395 2 13.5 220 197.320 225.000 2,025.000 1,225.000 3 16.5 140 155.470 4 14.5 190 130 225.000 498.182 381.421 70.057 702.515 157.628 183.370 148.495 5 17 16 160 162.445 6 7 13 210 B 2,025.000 225.000 1,225.000 625.000 625.000 225.000 18 204.295 134.545 218.245 169.420 150 858.197 1,636.607 1,870.130 9 12 200 10 15.5 190 31.136 Total The coefficient of determination (r) 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 gations) in a sales region where the selling price is $12.50? O 396,140 4 2(17.473) O 396.140 A 203.094) O 211.265 A 203.094) 0 211.265 2(17.473) 9 12 200 625.000 218.245 169.420 1,870.130 31.136 10 15.5 190 225.000 Total The coefficient of determination (r) 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 $12.507 O 396.140 + 2(17.473) O 396.140 +243.094) 0 211.265 + 2(3.094) O 211.265 + 2(17.473) What is the price elasticity of demand at a selling price of $12.50? -0.06 -0.05 0 -0.55 0 -0.83