Problem 13.73) Can you use movie critics’ opinions to forecast box office receipts on the opening weekend? The following data, stored in Tomatometer, indicate the Tomatometer rating, the percentage of professional critic reviews that are positive, and the receipts per theater ($thousands) on the weekend a movie opened for 10 movies:Movie Tomatometer Rating ReceiptsThe Mummy 16 7.8Zookeeper’s Wife 61 6.1Beatriz at Dinner 80 28.4The Hero 76 11.3Wonder Woman 93 24.8Baby Boss 52 13.3The Circle 15 2.9Dean 61 4.0Baywatch 20 5.1Churchill 38 1.9Source: “Top Box Office Movies – Rotten Tomatoes,” and “The Numbers – Weekend Box Office Chart for May 26th 2017,” bit.ly/2t0tqS6.Use the least-squares method to compute the regression coefficients b0 and b1.Interpret the meaning of b0 and b1 in this problem.Predict the mean receipts for a movie that has a Tomatometer rating of 55%.Should you use the model to predict the receipts for a movie that has a Tomatometer rating of 5%? Why or why not?Determine the coefficient of determination, r2, and explain its meaning in this problem.Perform a residual analysis. Is there any evidence of a pattern in the residuals? Explain.At the 0.05 level of significance, is there evidence of a linear relationship between Tomatometer rating and receipts?Construct a 95% confidence interval estimate of the mean receipts for a movie that has a Tomatometer rating of 55% and a 95% prediction interval of the receipts for a single movie that has a Tomatometer rating of 55%.Based on the results of (a)–(h), do you think that Tomatometer rating is a useful predictor of receipts on the first weekend a movie opens? What issues about these data might make you hesitant to use Tomatometer rating to predict receipts?Problem 13.74) Management of a soft-drink bottling company has the business objective of developing a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. To begin, management decided to develop a regression model to predict delivery time based on the number of cases delivered. A sample of 20 deliveries within a territory was selected. The delivery times and the number of cases delivered were organized in the following table and stored in Delivery.Customer Number of Cases Delivery Time (minutes) Customer Number of Cases Delivery Time (minutes)?1 ?52 32.1 11 161 43.0?2 ?64 34.8 12 184 49.4?3 ?73 36.2 13 202 57.2?4 ?85 37.8 14 218 56.8?5 ?95 37.8 15 243 60.6?6 103 39.7 16 254 61.2?7 116 38.5 17 267 58.2?8 121 41.9 18 275 63.1?9 143 44.2 19 287 65.610 157 47.1 20 298 67.3Use the least-squares method to compute the regression coefficients b0 and b1.Interpret the meaning of b0 and b1 in this problem.Predict the mean delivery time for 150 cases of soft drink.Should you use the model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Why or why not?Determine the coefficient of determination, r2, and explain its meaning in this problem.Perform a residual analysis. Is there any evidence of a pattern in the residuals? Explain.At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered?Construct a 95% confidence interval estimate of the mean delivery time for 150 cases of soft drink and a 95% prediction interval of the delivery time for a single delivery of 150 cases of soft drink.What conclusions can you reach from (a) through (h) about the relationship between the number of cases and delivery time?Problem 14.72) The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved and the number of pieces of large furniture as the independent variables and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving.State the multiple regression equation.Interpret the meaning of the slopes in this equation.Predict the mean labor hours for moving 500 cubic feet with two large pieces of furniture.Perform a residual analysis on your model and determine whether the regression assumptions are valid.Determine whether there is a significant relationship between labor hours and the two independent variables (the number of cubic feet moved and the number of pieces of large furniture) at the 0.05 level of significance.Determine the p-value in (e) and interpret its meaning.Interpret the meaning of the coefficient of multiple determination in this problem.Determine the adjusted r2.At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.Determine the p-values in (i) and interpret their meaning.Construct a 95% confidence interval estimate of the population slope between labor hours and the number of cubic feet moved.Compute and interpret the coefficients of partial determination.What conclusions can you reach concerning labor hours?Problem 14.74) A sample of 61 houses recently listed for sale in Silver Spring, Maryland, was selected with the objective of developing a model to predict the asking price (in $thousands), using the living space of the house (in square feet) and age (in years). The results are stored in Silver Spring Homes.Fit a multiple regression model.Interpret the meaning of the slopes in this model.Predict the mean asking price for a house that has 2,000 square feet and is 55 years old.Perform a residual analysis on your model and determine whether the regression assumptions are valid.Determine whether there is a significant relationship between asking price and the two independent variables (house size and age) at the 0.05 level of significance.Determine the p-value in (e) and interpret its meaning.Interpret the meaning of the coefficient of multiple determination in this problem.Determine the adjusted r2.At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.Determine the p-values in (i) and interpret their meaning.Construct a 95% confidence interval estimate of the population slope between asking price and the living space of the house. How does the interpretation of the slope here differ from that in Problem 13.76 on page 471?Compute and interpret the coefficients of partial determination.What conclusions can you reach about the asking price?
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