The director of the Riley County, Kansas, library system would like to forecast evening patron usage for next week. Below are the data for the past 4 weeks: Week 1 Week 2 Week 3 Week 4 Mon 210 215 220 225 Tue Wed Thu Fri Sat 215 160 180 213 165 185 178 250 180 250 176 260 220 175 190 260 225 176 190 178 a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places). Mon Tue Wed Thu Fri Sat Day of the week Seasonal index b) Let x = 1 for Monday of Week 1. If the trend equation for this problem is: y=201.74 +0.18x, the forecast for each day of week 5 is (round your responses to the nearest whole number): Mon Tue Wed Thu Day of week 5 Forecast Fri Sat

The director of the Riley County, Kansas, library system would like to forecast evening patron usage for next week. Below are the data for the past 4 weeks: Week 1 Week 2 Week 3 Week 4 Mon 210 215 220 225 Tue Wed Thu Fri Sat 215 160 180 213 165 185 178 250 180 250 176 260 220 175 190 260 225 176 190 178 a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places). Mon Tue Wed Thu Fri Sat Day of the week Seasonal index b) Let x = 1 for Monday of Week 1. If the trend equation for this problem is: y=201.74 +0.18x, the forecast for each day of week 5 is (round your responses to the nearest whole number): Mon Tue Wed Thu Day of week 5 Forecast Fri Sat

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 29P: The file P13_29.xlsx contains monthly time series data for total U.S. retail sales of building...

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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?
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?
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 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_26.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Does it make much of an improvement over the model in part b?
1. The number of bushels of apples sold at a roadside fruit stand over a 12-day period were PROBLEMS as follows: Day Numbar Sold Day Number Sold 25 35 31 29 33 32 38 10 40 37 32 34 11 37 12 If a two-period moving average has been used to forecast sales, what were the daily forecasts starting with the forecast for day 3? If a four-period moving average has been used, what were the forecasts for eacn uay starting with day 5? Plot the original data and each set of forecasts on the same graph. Which forecast has the greater tendency to smooth? Which forecast has the better ability to respond quickly to changes? What does use of the term sales instead of demand imply? b. C. 2. If exponential smoothing with a = .4 had been used to forecast daily sales for apples in Problem 1, determine what the daily forecasts would have been. Then, plot the original data, the exponential forecasts, and a set of naive forecasts on the same graph. Based on a visual comparison, is the naive more accurate or…
The director of the Riley County, Kansas, library system would like to forecast evening patron usage for next week. Below are the data for the past 4 weeks: Mon Tue Wed Thu Fri Sat Week 1 210 178 250 215 160 180 Week 2 215 180 250 213 165 185 Week 3 220 176 260 220 175 190 Week 4 225 178 260 225 176 190 a) Calculate a seasonal index for each day of the week (enter your responses rounded to three decimal places). Day of the week Mon Tue Wed Thu Fri Sat Seasonal index
Use exponential smoothing with a=0.2 and a=0.5 to generate forecasts for periods 2 through 6. Use MAD and MSE to decide which of the two models produced a better forecast. Period Actual Forecast 1 15 17 2 18 3 14 4 16 5 13 6 16
Consider the monthly sales data of a company for last year as well as first six-month data for current year. Use a three- quarter weighted moving average, Forecast the sales of company for 3rd Quarter of current year. Use Weights of 4/7, 2/7 and 1/7, giving more weight to more recent data. Note, the 1ist quarter is Jan, Feb and March, 2nd quarter is Apr, May, June, 3rd quarter is July, Aug and Sept, and 4th quarter is Oct, Nov and Dec. Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Last Yr 100 125 135 175 185 200 150 140 130 200 225 250 Current Yr 125 135 135 190 200 190
1. The number of bushels of apples sold at a roadside fruit stand over a 12-day period were as follows: Day Numbar Sold Day Number Sold 25 35 31 8. 32 29 9. 10 38 33 34 37 40 37 32 11 12 If a two-period moving average has been used to forecast sales, what were the daily forecasts starting with the forecast for day 3? If a four-period moving average has been used, what were the forecasts for eacn uay starting with day 5? Plot the original data and each set of forecasts on the same graph. Which forecast has the greater tendency to smooth? Which forecast has the better ability to respond quickly to changes? What does use of the term sales instead of demand imply? a. b. C. 123 4 56
Consider the monthly sales data of a company for last year as well as first six month data for current year. Use a three- quarter weighted moving average, Forecast the sales of company for 3rd Quarter of current year. Use Weights of 4/7, 2/7 and 1/7, giving more weight to more recent data. Note, the 1ist quarter is Jan, Feb and March , 2nd quarter is Apr, May, June, 3rd quarter is July, Aug and Sept, and 4th quarter is Oct, Nov and Dec. Month Jan Feb Mar April May June July Aug Sept Oct Nov DecLast Year 100 125 135 175 185 200 150 140 130 200 225 250Current Year 125 135 135 190 200 190