Consider the following time series: Quarter Year 1 Year 2 Year 3 80 74 65 69 61 51 48 50 43 68 71 82 a. Construct a time-series plot. What type of pattern exists in the data? Is there an indication of a seasonal pattern? b. Use multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtrl = 1 if quarter 1,0 else; Qtr2 = 1 if quarter 2,0 else; Qtr3 = 1 if quarter 3,0 else. c. Compute the quarterly forecasts for next year.
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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 following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.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. 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: Quarter Year 1 Year 2 Year 3 1 66 63 57 2 48 40 50 3 59 61 54 4 73 76 67 (a) Choose a time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? Is there an indication of a seasonal pattern? (b) Use a multiple linear 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. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300). ŷ = ?? + ?? Qtr1 +?? Qtr2 + ?? Qtr3 (c) Compute the quarterly forecasts for next year. Year Quarter Ft 4 1 4 2 4 3 4 4Consider 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 (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 intermediate calculation. Year Quarter Ft 4 1 4 2 4 3 4 4 (d) Use a multiple…
- Consider the following time series. Quarter Year 1 Year 2 Year 3 1 71 68 62 2 49 41 51 3 58 60 53 4 78 81 72 Construct a time series plot. What type of pattern exists in the data? Use a multiple linear 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. Compute the quarterly forecast for the next year.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 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 = + Qtr1 + Qtr2 + Qtr3 + t Compute the quarterly forecasts for next year. If required, round your answers to two decimal places.Quarter 1 forecast = Quarter 2 forecast = Quarter 3 forecast = Quarter 4 forecast =Which of the following time-series forecasting methods would not be used to forecast a time series that exhibits a linear trend with no seasonal or cyclical patterns? a. Dummy variable regression b. Linear trend regression c. Multiplicative Winter's method d. Holt Winter's double exponential smoothing e. Both A and D
- 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 A. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Q1 if quarter 1, 0 otherwise; Q2 if quarter 2, 0 otherwise; Q3 if quarter 3, 0 otherwise. B. Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (A) to capture seasonal effects and create a variable "Trend" such that T=1 for quarter 1 in year 1, T=2 for quarter 2 in year1,.... T=12 for quarter 4 in year 3.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 minimizesMSE for this time series.c. What is the forecast for t 5 6?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.