Apply the exponential smoothing technique with exponential smoothing constant a = 0.3 to the following data for period 1 through 10 and compute forecasting errors also. Time Period 12 3 4 5 6 789 10 Gasoline Sales 39 37 61 58 | 18 | 56 | 82 27 | 41 | 69
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?The below time series gives the indices of Industrial Production in U.S for 10 consecutive years. Year IP 1 79.62 2 86.54 3 88.14 4 89.23 5 93.45 6 97.4 7 99.34 8 96.98 9 100.22 10 103.56 Construct a time series plot. What type of pattern exists in the data? Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. What is the forecast for t = 11?The below time series gives the indices of Industrial Production in U.S for 10 consecutive years. Year IP 1 79.62 2 86.54 3 88.14 4 89.23 5 93.45 6 97.4 7 99.34 8 96.98 9 100.22 10 103.56 Construct a time series plot. What type of pattern exists in the data? Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. c. What is the forecast for t = 11?
- The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and it’s Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following : a. E(x) b. P(x=1) c. P(x=4) d. P(x6) e. P(2x5)Suppose that index model for Stocks A and B is estimated from excess returns with the following results : Ra 0.04 +0.6Rm+ea , Rb = - 0.04 + 1.3Rm + eb Risk on the market is 30% , R-squared of A is 30%R - squared of B is 40% , security A residual variance is1. Consider the following time series: a. Construct a time series plot. What type of pattern exists in the data? b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
- Respond to each of the items using the following time series data. Period Demand 1 20 2 46 3 20 4 9 5 17 6 8 7 19 8 34 9 39 10 4 11 32 12 23 13 10 14 27 b. Compute all possible forecasts using exponential smoothing with a smoothing coefficient (α) of 0.3. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Period Demand Exponential Smooth Error Absolute Error 1 20 2 46 3 20 4 9 5 17 6 8 7 19 8 34 9 39 10 4 11 32 12 23 13 10 14 27 15 c. Compute all possible forecasts using exponential smoothing with a smoothing coefficient (α) of 0.7. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Respond to each of the items using the following time series data. Period Demand Exponential Smooth Error Absolute Error 1 20 2 46…The values of Alabama building contracts (in $ millions) for a 12 -month period follow. 240 350 240 260 280 320 220 310 240 310 240 240 A. Compare the three-month moving average approach with the exponential smoothing forecast using a=0.2 (to 2 decimals). MSE (3-Month) _______ MSE ( a=0.2) __________ Using only the errors for months 4 to 12, the MSE for exponential smoothing is: MSE ( a=0.2) __________ C. Using the approach that provides more accurate forecasts based on MSE, what is the forecast for the next month (to the nearest whole number)? $ _______millionConsider the following time series data. Month 1 2 3 4 5 6 7 8 9value 23 12 20 22 15 23 24 17 22 a. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 10.b. Use α = .2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 10.c. Compare the three-week moving average approach with the exponential smoothing approach using α = .2. Which appears to provide more accurate forecasts based on MSE?
- Consider the following time series data. (07)Month 1 2 3 4 5 6 7 8 9value 23 12 20 22 15 23 24 17 22 a. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 10.b. Use α = .2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 10.c. Compare the three-week moving average approach with the exponential smoothing approach using α = .2. Which appears to provide more accurate forecasts based on MSE?The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following: a. E(x) P(x=1) c. P(x= 4) d. P(x6) e. P(2x5)The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following: a. E(x) b. P(x=1) c. P(x= 4) d. P(x6) e. P(2x5)