The below data on the production volume x and total cost y (in dollars) for a particular manufacturing operation were used to develop the estimated regression equation y = 1,581.33 + 6.96x. Production Volume | Total Cost (units) (%) 400 4,100 450 5,100 550 5,300 600 5,800 700 6,300 750 6,900 (a) The company's production schedule shows that 500 units must be produced next month. What is the point estimate of the total cost (in dollars) for next month? (Round your answer to the nearest cent.) $| | x (b) Develop a 99% prediction interval for the total cost (in dollars) for next month. (Round your answers to the nearest cent.) $| | to$[ | x (c) If an accounting cost report at the end of next month shows that the actual production cost during the month was $6,300, should managers be concerned about incurring such a high total cost for the month? Discuss. Since $6,300 is (within /| the prediction interval, managers should [notbe V|7 concerned about incurring such a high total cost for one month. The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA Monthly Salary ($ ) 2.6 3,700 3.4 3,900 3.6 4,300 3.2 3,800 3.5 4,100 2.9 3,900 The estimated regression equation for these data is y = 2,479.73 + 459.46x and MSE = 19,695.95. (a) Develop a point estimate of the starting salary (in dollars) for a student with a GPA of 3.0. (Round your answer to the nearest cent). $ X (b) Develop a 95% confidence interval for the mean starting salary (in dollars) for all students with a 3.0 GPA. (Round your answers to the nearest cent). $ x to $ X (c) Develop a 95% prediction interval (in dollars) for Ryan Dailey, a student with a GPA of 3.0. (Round your answers to the nearest cent). $ X to $ XGiven are data for two variables, x and y. 11 15 18 20 13 19 30 (a) Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.) =-7.22 + 1.5873x (b) Compute the residuals. (Round your answers to two decimal places.) Residuals 6 3.70 -3.24 15 -3.59 18 19 -2.35 20 5.48 (c) Develop a plot of the residuals against the independent variable x. Residuals ON ANONAG Residuals Residuals Residuals GANON - 2 AN -4 10 15 20 25 10 15 20 10 15 20 25 10 15 20 C Do the assumptions about the error terms seem to be satisfied? The plot suggests a funnel pattern in the residuals indicating that the error term assumptions are not satisfied. The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are not satisfied. The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are satisfied. The plot suggests curvature in the residuals indicating that the error term assumptions are not satisfied. The plot suggests curvature in the residuals indicating that the error term assumptions are satisfied. (d) Compute the standardized residuals. (Round your answers to two decimal places.) Standardized Residuals 6 11 -0.76 15 13 18 19 Jx 20 30 ixSuppose data on advertising expenditures and revenue (both in thousands of dollars) for a certain restaurant follow. Advertising Expenditures Revenue 18 2 33 4 44 6 40 10 51 14 53 20 55 (a) Let x equal advertising expenditures (in thousands of dollars) and y equal revenue (in thousands of dollars). Use the method of least squares to develop a straight line approximation of the relationship between the two variables. (Round your numerical values to two decimal places.) x (b) Test whether revenue and advertising expenditures (both in thousands of dollars) are related at a 0.05 level of significance. (Use the F test.) State the null and alternative hypotheses. H.: B, =0 OH: B, = 0 O Ho: Po # 0 OH : P, 20 OH: B = 0 H : B #0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject Ho. We conclude that the relationship between advertising expenditures and revenue (both in thousands of dollars) is significant. O Reject Ho. We cannot conclude that the relationship between advertising expenditures and revenue (both in thousands of dollars) is significant. O Do not reject Ho. We cannot conclude tha vertising expenditures and revenue (both in thousands of dollars) is significant. Reject Ho. We conclude that the relationship between advertising expenditures and revenue (both in thousands of dollars) is significant.A large supermarket chain has invested heavily in data, technology, and analytics. Feeding predictive models with data from d in minutes). Arrival Time Shopping Time Arrival Time Shopping Time 6:00 p.m.) (minutes) 6:00 p.m.) (minutes) 23 38 23 18 15 14 (2) Develop a scatter diagram for arrival time as the independent variable. .. 8 8 8 8 8 8 Shopping Time (Minutes) topping Time (Minutes) Arrival Time (Minutes Before 6:00 p.m.) 9 8 8 8 8 8 5 : Arrival Time (Minutes Before 6:00 p.m. 20 40 60 80 100 120 140 30 40 50 20 40 60 80 100 120 140 10 20 30 40 Arrival Time (Minutes Before 6:00 p.m.) Shopping Time (Minutes) Arrival Time (Minutes Before 6:00 p.m.) Shopping Time (Minutes) (b) What does the scatter diagram developed in part (a) indicate about the r etween the two variables? The scatter diagram indicates a negative linear elationship between arrival time and shopping time. The scatter diagram indicates a positive linear relationship between arrival time and shopping time. The scatter diagram indicat Does there appear to be an outlier or influential observation? (Enter your answer as an ordered pair in the form x, y. If there is no answer, enter NONE.) x, y) = (114,22 Explain. (Select all that apply.) O The point is an outlier or influential observation because it has high leverage. The point is an outlier or influential observation because it does not fit the trend shown by the remaining data. sign. The point is an outlier or influential observation because if it were dropped from the data set, the intercept of the estimated regression line would change point is an outlier or influential observation because if it were dropped from the data set, the slope of the est ession line would change sign. There are no outliers or influential observations. (c) Using the entire data set, develop the estimated regression equation that can be used to predict the shopping time given the arrival time. (Let x = arrival time (in minutes before 6:00 p.m.), and let y = shopping time (in minutes). Round your numerical values to four decimal places.) (d) Use residual analysis to dete bservations are present. Which of the following eater than 2 or less than -2? (Select all that apply.) D (38, 36) O (52, 40 (114, 22) D (113, 55) (e) After looking at the scatter diagram n equation from part (c)-)The below data on the production volume x and total cost y (in dollars) for a particular manufacturing operation were used to develop the estimated regression equation = 1,581.33 + 6.96x. Production Volume | Total Cost (units) ($) 400 4,100 450 5,100 550 5,300 600 5,800 700 6,300 750 6,900 (a) The company's production schedule shows that 500 units must be produced next month. What is the point estimate of the total cost (in dollars) for next month? (Round your answer to the nearest cent.) $(5061.33 | (b) Develop a 99% prediction interval for the total cost (in dollars) for next month. (Round your answers to the nearest cent.) $| | tos x () If an accounting cost report at the end of next month shows that the actual production cost during the month was $6,300, should managers be concerned about incurring such a high total cost for the month? Discuss. Since $6,300 is (within /| the prediction interval, managers should [notbe v| concerned about incurring such a high total cost for one month. The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA Month(l;)salarv 2.6 3,700 3.4 3,900 3.6 4,300 3.2 3,800 3.5 4,100 2.9 3,900 The estimated regression equation for these data is = 2,479.73 + 459.46x and MSE = 19,695.95. (a) Develop a point estimate of the starting salary (in dollars) for a student with a GPA of 3.0. (Round your answer to the nearest cent). $|3766.21 X (b) Develop a 95% confidence interval for the mean starting salary (in dollars) for all students with a 3.0 GPA. (Round your answers to the nearest cent). $(3525.15 X to$[406945 | (c) Develop a 95% prediction interval (in dollars) for Ryan Dailey, a student with a GPA of 3.0. (Round your answers to the nearest cent). $[3480.75 X to$(432736 | x Given are data for two variables, x and y. 11 15 7 13 19 30 (a) Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.) y = -7.22 + 1.5873x (b) Compute the residuals. (Round your answers to two decimal places.) * ; Residuals 3.70 11 -3.24 15 13 -3.59 18 19 -2.35 20 30 5.48 lv (c) Develop a plot of the residuals against the independent variable x. 6T Residuals Residuals ANONA Residual Residuals 10 15 20 25 10 15 20 10 15 20 25 10 15 20 Do the assumptions about the error terms seem to be satisfied? The plot suggests a funnel pattern in the residuals indicating that the error term assumptions are not satisfied. The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are not satisfied. The plot suggest sumptions are satisfied The plot suggests curvature in t ssumptions are not satisfied. The plot suggests curvature in the residuals indicating that the error term assumptions are satisfied. (d) Compute the standardized residuals. (Round your answers to two decimal places.) Standardized Residuals 0.87 11 -0.76 15 13 0.84 18 19 -0.55 x 20 30 1.29 XYou may need to use the appropriate technology to answer this question. Suppose data on advertising expenditures and revenue (both in thousands of dollars) for a certain restaurant follow. Advertising Expenditures Revenue 1 18 2 33 4 44 6 40 10 51 14 53 20 55 (a) Let x equal advertising expenditures (in thousands of dollars) and y equal revenue (in thousands of dollars). Use the method of least squares to develop a straight line approximation of the relationship between the two variables. (Round your numerical values to two decimal places.) y= 29.20 + 1.57x X (b) Test whether revenue and advertising expenditures (both in thousands of dollars) are related at a 0.05 level of significance. (Use the F test.) State the null and alternative hypotheses. OH : B , # 0 Ha: P1 = 0 OH: B, = 0 OH: B, 20 OH: Bo = 0 H : Bo # 0 Find the value of the test statistic. (Round your answer to two decimal places.) 2.015 Find the p-value. (Round your answer to three decimal places.) p-value = 0.100 XA large supermarket chain has in d heavily in data, technology, and analytics. Feeding predictive models with data from an Arrival Time Shopping Time Arrival Time (minutes) Shopping Tim 6:00 p.m.) 6:00 p.m.) ( minutes ) 58 23 38 36 23 14 57 35 83 16 52 16 98 23 39 31 24 13 25 23 27 131 (a) Develop a scatter diagram for arrival time as the Ind indent variable. 8 8 8 8 By 8 . . Shopping Time (Minutes) shopping Time (Minutes) Arrival Time (Minutes Before 6:00 p.m.) Arrival Time (Minutes Before 6:00 p.m. . .. . 20 20 40 60 80 100 120 140 30 40 50 60 20 40 60 80 100 120 140 10 20 30 40 60 Arrival Time (Minutes Before 6:00 p.m.) Shopping Time (Minutes) Arrival Time (Minutes Before 6:00 p.m.) Shopping Time (Minutes) (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a nonlinear rela onship between arrival time and shopping time. The scatter diagr val time and shopping tim The scatter diagram indicates a positive lin ip between arrival time and shopping time. The scatter diagram indicates no apparent onship between arrival time and shopping time. Does there appear to be an outlier or influential observation? (Enter your answer as an ordered pair in the form x, y. If there is no answer, enter NONE.) (x, y) = ( 114,22 Explain. (Select all that apply.) The point is an outlier or influential obs vation because it has high leverage. The point is an outlier or influential observation because it does not fit the trend shown by the remaining data. The point is an outlier or influential observation because if it were dropped from the data set, the intercept of the estima he would change The point is an outlier or influential observation because if it were dropped from the data set, the slope of the e There are no outliers or Influential observations. (c) Using the entire data set, develop the estimated regress cal values to four decimal places.) 9- 14.4401 + 0.2477x (d) Use residual analysis to determ bservations are present. Which of the following point ter than 2 or less than -2? (Select all that apply.) D (38, 36) O (52, 40) (114, 22) (113, 55) (e) After looking at the scatter diagram in part (a), suppose you were able to visually identify whata uation from part (c).) - 13.4457 + 0.2811 x Compare the estimated slope for the new estimated regression equation to the estimated slope obtained in part (c). Does this approach co reached in part (d)? Explain. Yes, because the value of the slope of ecause the value of the slope of the fitted line did not change after removing the influential observation. There are no outliers or influential observations