d). - Why are there months when the Absolute Value of Error is very low and months when it is much higher? Calculate the Mean Absolute Deviation (MAD), the Mean Squared Error (MSE) and the e) Mean Absolute Percent Error (MAPE) for the Naïve Forecast you created for Product X from March/2019 to January/2020 (not from February/2019 to January/2020).
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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 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_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 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?
- 3. Quarterly sales of a car dealer exhibit an almost constant mean over time, but sales fluctuate depending on the quarter of the year (exhibits seasonality). Quarter Q1 - Spring Q2 - Summer Q3 - Fall Q4 - Winter Mean Year 1 32 74 53 22 45.25 Year 2 30 71 63 15 44.75 Year 3 35 83 45 19 45.5 (a) Using three years' worth of quarterly data that is provided, develop a set of seasonal factors that could be used to forecast car sales (b) Forecast car sales in each of the four quarters (Q1-Q4) of the following year (Year 4), using these seasonal factors.Year Quarter Sales Isolated trend 2016 1 18 2016 2 28 2016 12 2016 4 8 2017 1 16 2017 2 38 2017 3 24 2017 4 17 2018 1 34 A 2018 2 40 2018 29 2018 4 26 2019 1 42 2019 2 52 2019 40 2019 4 34 43.75 2020 1 46 2020 2 58 The table contains decomposition figures of the quarterly sales in millions of Rands for a large store. The value of A isThe following table shows the three-period moving average and five-period moving average for monthly sales of Budget Furniture's during 2019. Moving averages of Budget Furniture's Time period Months Sales Three-period moving average (rounded off to Five-period moving average four decimals) R'millions 1 Jan 7 5.0000 6.2 February 5.6667 6.6 March 5 7.0000 B 4 April 8.3333 8.2 May 7 9.3333 8.4 June 8.3333 9.6 7 July 12 8.6667 9.6 August 4 A 9.2 September 10 10.6667 10 October 13 10.6667 11 November 9 12 December 10 The seasonal index for the month of February in 2019 is: LO
- Year Season Sales 2018 Winter 40 2018 Spring 29 2018 Summer 31 2018 Fall 40 2019 Winter 102 2019 Spring 87 2019 Summer 96 2019 Fall 132 2020 Winter 105 2020 Spring 93 2020 Summer 105 2020 Fall 117 2021 Winter 141 2021 Spring 39 2021 Summer 114 2021 Fall 123 What is the slope of the trend equation obtained by linear regression? Round to two decimal digits. What is the intercept of the trend equation obtained by linear regression? Round to two decimal digits. What is the seasonal index for Spring? Round to two decimal digits. The quarter number for Winter of 2018 is 1. What is the quarter number for Spring of 2025? What is the trend based forecast for Spring of 2025. Round to a whole number. What is the seasonally adjusted trend based forecast for Spring of 2025? Please do not use excel to find the slope and intercept, thank you so much!Given the demand data, answer the following questions below. Year Sales 1 - 123 2 - 118 3 - 109 4 - 112 5 -100 6 -110 7 -124 8 - ? What will be the forecast demand in Year 8 using Naïve method?a.) 120b.) 110c.) 115d.) 124The following table shows the past two years of quarterly sales information. Assume that there are both trend and seasonal factors and that the seasonal cycle is one year. QUARTER SALES QUARTER SALES 1. 211 5 155 235 6 198 3 206 7 154 4 190 8 142 Use regression and seasonal indexes to forecast quarterly sales for the next year. (Do n ot round intermediate calculations. Round your answers to the nearest whole number.) Answer is complete but not entirely correct. Quarter Forecast 142 8 157 8 121 8 10 11 12 103