a. Using the following, forecast the sales for the months up to January the following year:- i. A simple three month moving average. ii. A three period weighted moving average using weights of 1, 2 and 3. Assign the highest weight to the most recent data. iii. Exponential Smoothing when a= .6 and the forecast for March is 350.
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- Under what conditions might a firm use multiple forecasting methods?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_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 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?
- 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_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 demand (in number of units) for Apple iPad over the past 6 months at BestBuy is summarized below. Month Nov 2019 Dec 2019 Demand 45 48 Jan 2020 50 Feb 2020 Mar 2020 Apr 2020 42 46 51 Consider the following three forecasting methods: • Two-month weighted moving average, with weights 6 and 2 (more weight assigned to more recent data) Exponential smoothing with a = 0.7. Let the initial forecast for Nov 2019 be 46. • A trend line projection in the form ŷ = a+bx . To simplify computations, transform the value of x (time) to simpler numbers – designate Nov 2019 as x=1, Dec 2019 as x= 2, etc. (a ) For each of the above methods, forecast the demand of Apple iPad for May 2020. (b) Consider only the two-month weighted moving average method, compute the MAD measure and the MSE measure using the data from Jan 2020. (c) Use the trend line to forecast the demand of Apple iPad for Dec 2020. Give your opinion regarding the reliability of the forecast.
- 4. The sales (in millions of dollars) for an 18-month period are as follows. Month Sales Month Sales 1 600 600 775 10 775 3 600 11 600 4 650 12 575 700 13 625 800 14 650 550 15 600 8 775 a. Compare a three-month moving average forecast with an exponential smoothing forecast. Use a = 0.1. Which provides the better forecasts based on MSE? b. Find the forecast for the next month using the best forecast method. 2.Consider the following time series data. Week 1 2 3 4 5 6 Value 18 12 15 11 18 13 Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. (a) Mean absolute error If required, round your answer to one decimal place. (b) Mean squared error If required, round your answer to one decimal place. (c) Mean absolute percentage error If required, round your intermediate calculations and final answer to two decimal places. (d) What is the forecast for week 7?Please consider the following information and make forecasts for January, February, March, and April of Year 2. Use second-order polynomial regression to make forecasts. Adjusted seasonal index Actual sales Deseasonalized sales 836 825 Year 1 Year 2 January February March April May June July August September October November December January February March April 0.72 0.75 1:22 1.48 1 1.23 0.7 0.78 0.92 1.13 1.28 1.33 0.72 0.75 1.22 1.48 1220 1319 1020 1184 685 641 875 1008 1068 1141