Instructions: Answer all the questions in the homework The number represented in parenthesis, e.g. (2pt) represents two points for the question You are welcome to use excel. Doing so, please take pics/screenshot and copy into the document file Do not submit excel files. Please submit only a single pdf file of your answers in canvas by the due date and time 1. Problem 1(10pt) DigiSonic has been the leading supplier of Blu-Ray discs to the U.S. movie studios since 2006. For nearly a decade, the sales of Blu-Ray discs were high thanks to the popularity of the format. However, the demand for the Blu-Ray discs started to decrease last year, as customers started to watch movies from online platforms such as Amazon Instant Video, Google Play Movies and Netflix. DigiSonic is in critical need of a better forecasting method. They need your help to evaluate alternative forecasting methods and provide suggestions. The following table contains the past 12 months' sales data (Note: Month 1 refers to sales made 12 months ago, month 12 refers to sales made last month.) a. Use a 3-month simple moving average to forecast sales. Compute the Mean Absolute Error (MAE) and the Mean Square Error (MSE) of the forecasts for months 4 to 12. (4pt) b. Using a 3-month weighted average method with weights of 0.5,0.3 and 0.2 (which are the weights for the most recent, next most recent, and the third most recent month, respectively). Again, compute the MAE and MSE of the forecasts with the weighted moving average method. (3pt) c. Using MAE as the measure, compare the performance of the two forecasting methods (moving average, weighted moving average). Which forecasting method is better? (ii) If you use MSE as the measure (instead of MAE) to compare the performance of the two forecasting methods (moving average, weighted moving average), which forecasting method is better? (3pt) 2. Problem 2 (15pt) DigiSonic would also like to explore a more sophisticated forecasting method. They want you to consider exponential smoothing. a. Using simple exponential smoothing, compute three sets of forecasts for the sales of DigiSonic's Blu-Ray discs, corresponding to values of 0.2,0.5 and 0.8 . Assume that the forecast for month 1 is 1376.(8pt) b. To visually see the difference between forecasts and actual demand, plot the actual demand as well as the three simple exponential smoothing forecasts computed in the same graph. Identify which value of produces the most responsive forecast? What is the implication of this finding? (4pt) c. Calculate the MAE and Mean Absolute Percentage Error (MAPE) using the forecast errors for each of these three sets of forecasts. Which value seems to be most appropriate and explain why. (3pt) 3. Problem 2(15pt) DigiSonic observes from the sales data that sales of Blu-Ray discs have been decreasing over the last year. As mentioned earlier, this is due to the increasing popularity of online movie platforms among customers. DigiSonic wants to incorporate this decreasing trend into its forecasts. You have learned that the double exponential smoothing method accounts for such trends in the data. a. Use the double (trend-adjusted) exponential smoothing method to forecast sales for months 2 to 13 (i.e., F2 to F13 ), assuming S1=1376 and T1=25 and set =0.8 and =0.2. (10pt) b. Create a plot showing the actual sales, the double exponential smoothing forecast, and the forecast obtained using simple exponential smoothing in Problem 2 with =0.8 for months 1 to 12 on the same graph. (3pt) c. Compute MAE and MAPE for months 2 through 12 for the double exponential smoothing forecast and compare them with those of simple exponential smoothing in problem 2(c). Based on your calculations, is single or double exponential smoothing a better approach in this specific case? Why? (3pt) d. Develop a simple linear regression model using month as the independent variable to forecast the DigiSonic's Blu-Ray disc sales for month 13 (i.e., F13). Compare this forecast to the forecast obtained in part (a) for sales in month 13. Based on this, explain the difference between the two methods (regression, double exponential smoothing). (9pt)