Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 16 11 17 14
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- Consider the following time series data.
Week |
1 |
2 |
3 |
4 |
5 |
6 |
Value |
18 |
13 |
16 |
11 |
17 |
14 |
- Construct a time series plot. What type of pattern exist in the data?
- Develop a three-week moving average for this time series. Compute MSE and forecast for week 7.
- Use a = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and forecast for week 7.
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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?consider the following time series data.Month 1 2 3 4 5 6 7Value 24 13 20 12 19 23 15a. compute MSe using the most recent value as the forecast for the next period. Whatis the forecast for month 8?b. compute MSe using the average of all the data available as the forecast for the nextperiod. What is the forecast for month 8?c. Which method appears to provide the better forecast?Consider the following time series data Week 1 2 3 4 5 6 Value 18 13 16 11 17 14 a. Construct a time series plot. What type of pattern exists in the data?b. Develop the three-week moving average forecasts for this time series. compute MSE and a forecast for week 7.c. Use α = .2 to compute the exponential smoothing forecasts for the time series.Compute MSE and a forecast for week 7.d. Compare the three-week moving average approach with the exponentialsmoothing approach using α = .2. Which appears to provide more accurate forecasts based on MSE? explain.e. Use a smoothing constant of α = .4 to compute the exponential smoothing forecasts. does a smoothing constant of .2 or .4 appear to provide more accurate forecasts based on MSE? explain.
- Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6 7 2 2 3 6 3 3 5 6 4 5 7 8 Choose the correct time series plot. (i) (ii) (iii) (iv) - Plot (iii) What type of pattern exists in the data?- Horizontal Pattern with Seasonality Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)Value = fill in the blank 3 + fill in the blank 4 Qtr1 + fill in the blank 5 Qtr2 + fill in the blank 6 Qtr3 + fill in the blank 7 t Compute the quarterly forecasts for next year. If…Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6 7 2 0 1 4 3 3 5 6 4 5 7 8 (a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300). If the constant is "1" it must be entered in the box. Do not round intermediate calculation. ŷ = + Qtr1 + Qtr2 + Qtr3 (c) Compute the quarterly forecasts for next year based on the model you developed in part (b). If required, round your answers to three decimal places. Do not round…Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 16 11 17 14 a. Construct a time series plot. What type of pattern exists in thedata?b. Develop the three-week moving average forecasts for this timeseries. compute MSE and a forecast for week 7.c. Use α= .2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7.d. Compare the three-week moving average approach with theexponential smoothing approach using α = .2. Which appears to provide more accurate forecasts based on MSE? explain.e. Use a smoothing constant of α = .4 to compute the exponentialsmoothing forecasts. does a smoothing constant of .2 or .4 appearto provide more accurate forecasts based on MSE? explain.
- Which of the following time series forecasting methods would not be used to forecast seasonal data?Consider the following time series data: 1 2 3 4 5 6 7 26 15 22 14 21 25 17 PART 1.Compute MSE using the most recent value as the forecast for the next period and then calculate the forecast for month 8. PART 2.Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for month 8?Consider the following time seriesweek 1 2 3 4 5 6 value 18 13 16 11 17 14 a) Construct a time series plot? What type of pattern exists in the datab) Develop the three week moving average forecasts for this time series, then compute the measures of forecasts accurecy
- Below you are given the first five values of a quarterly time series. The multiplicative model is appropriate and a four-quarter moving average will be used. Year Quarter Time Series Value Yt 1 1 36 2 24 3 16 2 4 20 1 44 An estimate of the combined trend-cycle component (T2Ct) for Quarter 3 of Year 1 (used for estimating the de-trended values), when a four-quarter moving average is used, is a. 24. b. 26. c. 28. d. 25.Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 15 13 15 15 (a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? (b) Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Do not round intermediate calculations. If required, round your answers to two decimal places. Week Value Forecast 1 18 2 13 3 15 4 13 5 15 6 15 MSE: The forecast for week 7: (c) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Do not round intermediate calculations. If required, round your answers to two decimal places. Week Value Forecast 1 18 2 13 3 15 4 13 5 15 6 15 MSE: The forecast for week 7: (d) Compare the three-week moving average forecast with the…consider the following time series data.Month 1 2 3 4 5 6 7Value 24 13 20 12 19 23 15construct a time series plot. What type of pattern exists in the data?a. develop the three-week moving average forecasts for this time series. compute MSeand a forecast for week 8.b. Use a = .2 to compute the exponential smoothing forecasts for the time series. compute MSe and a forecast for week 8.c. compare the three-week moving average approach with the exponential smoothing approach using a = .2. Which appears to provide more accurate forecasts based on MSe?d. Use a smoothing constant of a = .4 to compute the exponential smoothing forecasts.does a smoothing constant of .2 or .4 appear to provide more accurate forecasts basedon MSe? explain