5. (10 points) Regression Models for Forecasting Consider the following time series plot of monthly data (January to December) for three years. a. (4 points) What type of pattern exists in this time series?
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A statistical program is recommended. Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 12 14 15 2 10 11 14 3 11 13 14 4 13 15 16 (a) Construct a time series plot. What type of pattern exists in the data? The time series plot shows a horizontal pattern and no seasonal pattern in the data. The time series plot shows a linear trend and no seasonal pattern in the data. The time series plot shows a horizontal pattern, but there is also a seasonal pattern in the data. The time series plot shows a linear trend and a seasonal pattern in the data. (b) Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data. (Round your numerical values to two decimal places.) x1 = 1 if quarter 1, 0 otherwise; x2 = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise (c) Compute the quarterly forecasts for next year. (Round your answers to one decimal place.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast
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Consider the following quarterly time series. Quarter Year 1 Year 2 Year 3 1 920 1,112 1,246 2 1,056 1,156 1,302 3 1,128 1,124 1,254 4 992 1,078 1,198 a. Construct a time series plot. 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. c. Compute the quarterly forecasts for next year based on the model developed in part (b).
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