6. Consider the following data table. (12 Points) a) Forecast demand using exponential smoothing with an alpha of 0.25, and an initial forecast of 128.0 for period 1. b) Calculate the MAD and MSE. Period Real demand 2 138 3 129 4 140 5 133A
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- Under what conditions might a firm use multiple forecasting methods?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 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_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 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?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_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 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?9) Gasoline sales Times Series week sales (1000s of gallons 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 With the above gasoline time series data, show the exponential smoothing forecast using alpha = 0.1 i)Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of Alpha= 0.1 or alpha=0.2 for the gasoline sales time series? ii)Are the results the same if you apply MAE as the measure of accuracy? iii)What are the results if MAPE is used?
- The following monthly sales of chocolate boxes (in thousands of AUS dollars) have been recorded for January, February, March, and April, respectively: 9.5, 8, 9, 9. Examining the forecasting accuracy for the month of April only: Explain which of the following forecasting method would you recommend: (i) the Naïve method, (ii) the Average method, or (iii) the Simple exponential smoothing method (assuming alpha= 0.8 and initial state (in December) of 8.5)?Corporate triple-A bond interest rates for 12 consecutive months follow. Month 1 2 3 4 5 6 7 8 9 10 11 12 Value 9.5 9.3 9.4 9.6 9.8 9.7 9.8 10.5 9.9 9.7 9.6 9.6 a. Construct a time series plot. What type of pattern exists in the data? b. Develop the three-month moving averages for this time series. Compute MSE. c. Compute MAE. d. Compute MAPE. e. What is the three-month moving average forecast for the next month (month 13)?Prepare a forecast for period 6 using each of the following approaches: Period 1 2 3 4 5 Demand 60 65 55 58 64 A three-period moving average. A weighted average using weights of .50 (most recent), .20 and .30. Exponential smoothing with a smoothing constant of .40.
