The number of students enrolled in Spring Valley Elementary school has been steadily increasing over the past five years. The School Board would like to forecast enrolment for years 6 and 7 in order to better plan capacity. The past five years enrolment is indicated in the table below Year Enrollment 1 220 2 245 3 256 4 289 5 310 Assuming a linear trend, use the tabular method to derive values for: the slope the intercept Forecast period 6 enrollment

The number of students enrolled in Spring Valley Elementary school has been steadily increasing over the past five years. The School Board would like to forecast enrolment for years 6 and 7 in order to better plan capacity. The past five years enrolment is indicated in the table below Year Enrollment 1 220 2 245 3 256 4 289 5 310 Assuming a linear trend, use the tabular method to derive values for: the slope the intercept Forecast period 6 enrollment

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 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?
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.
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.
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 file P13_29.xlsx contains monthly time series data for total U.S. retail sales of building materials (which includes retail sales of building materials, hardware and garden supply stores, and mobile home dealers). a. Is seasonality present in these data? If so, characterize the seasonality pattern. b. Use Winters method to forecast this series with smoothing constants = = 0.1 and = 0.3. Does the forecast series seem to track the seasonal pattern well? What are your forecasts for the next 12 months?
The file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions. a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an exponential trend to the series. Second, use Holts method with optimized smoothing constants. b. Which of these two methods appears to provide the best forecasts? Answer by comparing their MAPE values.
The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next year. Comment on the performance of your model. What makes this time series more challenging to forecast?
At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
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 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?
The number of students enrolled in Spring Valley Elementary school has been steadily increasing over the past five years. The School Board would like to forecast enrolment for years 6 and 7 in order to better plan capacity. The past five years enrolment is indicated in table 3: Table 3 Year Enrollment 1 220 2 245 3 256 4 289 5 310 Assuming a linear trend, use the tabular method to derive values for: the slope the intercept Forecast period 6
Data collected on the yearly registrations for a Six Sigma seminar at the Quality College are shown in the following table: 3 8 9 6 7 6 3 7 10 11 Year Year Forecast (000) 1 5 1 5 2 5 4 4 4 5 11 Registrations (000) Use exponential smoothing with a smoothing constant of 0.4 to forecast the registrations at the seminar for years 2 through 12. To begin the procedure, assume that the forecast for year 1 was 5,000 people signing up (round your responses to one decimal place): 2 3 5 6 7 8 10 16 9 11 12 10 D 11 12 a) What is the MAD? Mean absolute deviation based on the forecast developed using the exponential smoothing method (with a smoothing constant (x) = 0.4 and a starting forecast of F₁ = 5) is thousand registrations (round your response to one decimal place). b) What is the MSE? The mean squared error based on the forecast developed using the exponential smoothing method (with a smoothing constant (x) = 0.4 and a starting forecast of F₁ = 5) is (round your response to two decimal…