The materials handling manager of a manufacturing company is trying to forecast the cost of maintenance for the company's fleet of over-the-road tractors. The manager believes that the cost of maintaining thetractors increases with their age. The following data was collected:Age(years)5.5where Y = Yearly maintenance cost in dollars and X = Age in years.5.55.55.05.05.06.06.06.5YearlyMaintenanceCost (S)1,3191,7491,7331,1951,4231,3811,5902,2221,687Age(years)5.01.51.5Y =7.07.02.02.02.0YearlyMaintenanceCost ($)1,894863882a. Use POM for Windows' least squares-linear regression module to develop a relationship to forecast the yearly maintenance cost based on the age of a tractor. (Enter your responses rounded to three decimalplaces and include a minus sign if necessary.)1,4642,0731,6781,1661,249

Answered: The materials handling manager of a…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section13.7: Exponential Smoothing Models

Problem 28P: The file P13_28.xlsx contains monthly retail sales of U.S. liquor stores. a. Is seasonality present...

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The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?
The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?
Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.
The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.
A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.
Management of a home appliance store wants to understand the growth pattern of the monthly sales of a new technology device over the past two years. The managers have recorded the relevant data in the file P13_05.xlsx. Have the sales of this device been growing linearly over the past 24 months? By examining the results of a linear trend line, explain why or why not.
The file P13_02.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a constant percentage each month and will continue to do so for at least the near future. a. Explain briefly whether the plot of the series visually supports the companys suspicion. b. By what percentage are sales increasing each month? c. What is the MAPE for the forecast model in part b? In words, what does it measure? Considering its magnitude, does the model seem to be doing a good job? d. In words, how does the model make forecasts for future months? Specifically, given the forecast value for the last month in the data set, what simple arithmetic could you use to obtain forecasts for the next few months?
A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of the year. The company has gathered the data given in the file P13_13.xlsx. Note that each observation corresponds to a particular truck. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
Rhonda Clark, a Slippery Rock, Pennsylvania, realestate developer, has devised a regression model to help determineresidential housing prices in northwestern Pennsylvania. The model was developed using recent sales in a particular neighbor-hood. The price ( Y ) of the house is based on the size (square foot-age 5 X ) of the house. The model is: Y = 13,473 + 37.65XThe coefficient of correlation for the model is 0.63.a) Use the model to predict the selling price of a house that is1,860 square feet.b) An 1,860-square-foot house recently sold for $95,000. Explainwhy this is not what the model predicted. c) If you were going to use multiple regression to develop such amodel, what other quantitative variables might you include?d) What is the value of the coefficient of determination in thisproblem?
The following time series represents the number of automobiles sold by a car dealership each of the past five months. t 1 2 3 4 5 Yt 7 12 10 13 14 (a) Construct a time series plot. What type of pattern exists in the data? The time series plot shows a linear trend.The time series plot shows a horizontal pattern. The time series plot shows a seasonal pattern.The time series plot shows a nonlinear trend. (b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. t = (c) What is the forecast for t = 6?
The classified department of a monthly magazine has used a combination of quantitative and qualitative methods to forecast sales of advertising space. Results over a 20-month period are as follows: Month Error Month Error 1 —8 11 1 2 —2 12 6 3 4 13 4 7 14 4 5 9 15 1 6 5 16 —2 7 0 17 —4 8 —3 18 —8 9 -9 19 —5 10 —4 20 —1 a. Compute a tracking signal for months 11 through 20. Compute

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