The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a perfect forecast of the future were available, what is the expected value with this perfect information?
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- 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 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?Under what conditions might a firm use multiple forecasting methods?
- 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?Sales of Cool-Man air conditioners have grown steadily during the past 5 years: (Round your answers to 2 decimal places.) Forecast Forecast Year Sales (a = 0.30) (a 0.90) 1 450 410.0 410.00 495 3 518 470.60 490.10 4 563 5 584 495.20 6 ? 1. The sales manager had predicted, before the business started, that year 1's sales would be 410 air conditioners. Using exponential smoothing with a weight of a = 0.30, complete the Forecast column to develop forecasts for years 2 through 6. What is the MADa=0.30 ? 2. Using exponential smoothing with a weight of a = 0.90, develop forecasts for years 2 through 6 by completing the Forcast column in the table. What is the MAD-0,90 ? 3. Using the trend projection method, develop a forecasting model to project sales for year 6. 2.
- A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. A. What percentage of adults do not conduct their banking online? B. What type of probability is the 25% mentioned above? Just write down the name of the probability. C. Construct a joint probability table showing all joint and marginal probabilities.For the E-Commerce Retail Sales (Million$) data given in the table below, provide estimates from the 1st Quarter (Q1) of 2016 to the 3rd Quarter (Q3) of 2017 by using two models: 1) Single Exponential Smoothing with α=0.3 2) Moving Average with k=2. Calculate MAPE for each model. Quarter Year Actual Q1 2016 86802 Q2 2016 92004 Q3 2016 93795 Q4 2016 124651 Q1 2017 99491 Q2 2017 106590 Q3 2017 108291 Compare two models above (Single Exponential Smoothing and Moving Average) based on their accuracies. Which forecasting method appears to be better? Using the model you choose, provide forecast for the 4th Quarter (Q4) of 2017. Assuming that this model is overestimating, find the actual value of the Q4 of 2017 based on MAPE value. Some residual graphs from the first forecast model (including wider range of E-Commerce Retail Sales data) are given below. What do these graphs tell about the model? Explain each graph.Discuss the following statement: “Economists are predicting that interest rates willcontinue to be under 10 percent for at least 15 years.”
- General Motors would like an estimate of the chance that Tesla will bring the cost of batteries down from $300 per kWh to $70. Dr. Tetlock has developed a process whereby selected teams are better estimators of future probabilities than experts, General Motors is willing to pay Dr. Tetlock for his teams' O scenarios O contingency plans O forecastsMovieflix, an online movie streaming service that offers a wide variety of award-winning TV shows, movies, animes, and documentaries, would like to determine the mathematical trend of memberships in order to project future needs. Year 2013 2014 2015 2016 2017 2018 2019 2020 2021Membership (000s) 17 16 16 21 20 20 23 25 24 1. What are the issues associated with qualitative forecasting, and how are these overcome?Sales of Volkwagen’s popular Beetle have grown steadily at autodealership in Nevada during the past 5 years (see table below).The sales manager had predicted before the new model wasintroduced that first-year sales would be 410 VWs. Usingexponential smoothing with a weight of α= .30, develop forecastfor years 2 through 6.Year Sales Forecast1 450 4102 4953 5184 5635 5846 ? 2. The following data come from regression line projections:Period Forecast Values Actual values1 410 4062 419 4233 428 4234 435 440 Compute the MAD and MSE.
