The following data set shows the weekly advertising expenditure and sales of 12 retail merchants selling face masks and beside it is the scatter diagram. 600 Cost Sales 40 385 500 20 400 25 395 400 20 365 30 475 300 50 440 40 490 200 20 420 50 560 100 40 525 25 480 0 50 510 0 10 20 30 40 50 60 Advertising Cost 1. For the equation of the regression line, find the value of bo and b₁. 2. Interpret the coefficients of the estimated regression line. 3. Find and interpret the R-square of the model. Sales
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Answer the following questions about the regression equation.
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- Consider the following set of ordered pairs. x 4 2 4 2 7 6 y 4 9 7 6 2 5 a) Calculate the slope and the y-intercept for the regression equation. b) Calculate the SST. c) Partition the SST into the SSR and the SSE.Find b0 and b1 and derive the regression line equation for the data below: x y 0 2 1 3 2 5 3 7 4 10 5 9Consider the following data set, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week. hours/weekx Gradey 5 58 8 63.2 8 73.2 9 68.6 9 70.6 11 68.4 13 81.2 14 86.6 17 100 20 100 The regression equation is y=3.04⋅x+42.33y=3.04⋅x+42.33.Explain what the value of the slope means in this situation, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week.Explain what the value of the y-intercept means in this situation.What is the predicted value for the final grade when a student spends an average of 15 hours each week on math?Grade = Round to 1 decimal place.
- The following data show the brand, price($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is y=23.043+2.7x , where x=price and y=overall score . Brand Price Score Bose 170 75 Scullcandy 160 71 Koss 95 62 Phillips/O'Neill 70 56 Denon 60 40 JVC 45 26 Round your answers to three decimal places. a. Compute SST,SSR , and SSE. SST (to 3 decimals) SSR (to 3 decimals) SSE (to 3 decimals) c. What is the value of the sample correlation coefficient? rxy=The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 21.592 + 0.324x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 76 B 150 69 C 95 61 D 70 56 E 70 38 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 21.258 + 0.327x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 74 B 150 73 C 95 59 D 70 54 E 70 40 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST= SSR= SSE= (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line did not provide a good fit as a large…
- The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 22.391 + 0.326x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 76 B 150 71 C 95 63 D 70 56 E 70 40 F 35 24 #1) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = SSR = SSE = #2) Compute the coefficient of determination r2.(Round your answer to three decimal places.) r2 = #2a) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) A) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. B) The least squares line provided a good fit as a large…The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 22.726 + 0.323x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 76 B 150 71 C 95 61 D 70 56 E 70 42 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST= ? SSR= ? SSE= ? (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2= ? Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line provided a good fit as a large proportion…The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 23.462 + 0.315x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 74 B 150 73 C 95 59 D 70 58 E 70 42 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST=SSR=SSE= (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) r2 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of…
- The following data give the percentage of women working in five companies in the retail and trade industry. The percentage of management jobs held by women in each company is also shown. %Working 68 45 73 55 62 %Management 50 21 65 47 34 Develop the estimated regression equation by computing the values b 0 and b 1.Enter negative values as negative numbers. Round your answer for the intercept to one decimal place, and your answer for the slope to two decimal places.y^ = + x Predict the percentage of management jobs held by women in a company that has 60% women employees. Round your answer to a whole percentage.The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows. The estimated regression equation for these data is y = 26.239 + 0.309x. (NEED ANSWERS FOR A and C)The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 25.130 + 0.309x, where x = price ($) and y = overall score. Brand Price($) Score A 180 78 B 150 69 C 95 63 D 70 56 E 70 42 F 35 28 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST= SSR= SSE= (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)