a. Plot the monthly sales data. Do you observe any trend, cycles or random variations? b. Forecast January sales using each of the following: a. Naïve method b. A 3-month moving average c. A 6-month weighted moving average using 0.1, 0.1, 0.1, 0.2, 0.2 and 0.3 with the heaviest weights applied to the most recent months d. Exponential smoothing using an x = 0.3 and a September forecast of 18. c. Compute the MAD and MAPE for the naïve method and 3-month moving average.
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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 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_28.xlsx contains monthly retail sales of U.S. liquor stores. 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?
- 2. Suppose that the University of the West had the following data of its growth of enrollment from 2016-2014. Year Enrollment 2006 3000 2007 3200 2008 3600 2009 3650 2010 4000 2011 4200 2012 4300 2013 4410 2014 4520 a. Forecast the 2015 enrollment using three-year weighted moving average forecast. b. Using smooth a = 0.30, forecast the 2015 enrollment. c. Using MAD, solve for the forecasting error at a = 0.10 d. Use four-year weighted moving average from 2006-20151. Consider the total production (and sales) of ice cream in Canada (in millions of liters) for the period 1995 until 2007 (from left to right): 341, 331, 317, 315, 321, 278, 298, 311, 302, 302, 335, 320, 285Fit a model to ice cream production data using each of the following techniques and forecast the 2008 production in each case. Also, plot the two moving average forecasts and the actual, the two exponential smoothing forecasts and the actual, and the linear trend and the actual (three graphs altogether). Two-year moving average. Four-year moving average. Exponential smoothing with smoothing constant = 0.2. Exponential smoothing with smoothing constant = 0.4. Linear trend (regression). f. Just by observing the plots, which of the above techniques would you use to forecast the ice cream production and why? (Hint: The plot overall closest to actual demand will be most accurate).g. Alternatively,computetheMADforeachforecastingtechniqueanddetermine the most accurate…3. A mobile phone store owner wants to predict the demand for mobile phones in October based on the following historical sales data: Month- April May June. July August September Number of phones sold. 100, 140- 110. 150. 120. 160- a. What is this month's forecast using Naive approach b. Using 3-Month Moving Average, develop forecasts for October's demand c. Using 5-Month Moving Average, develop forecasts for October's demand d. When making moving average forecasts, is it better to use a larger time span? -