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(b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to three decimal places.) x₁ - 1 if quarter 1, 0 otherwise; x₂-1 if quarter 2, 0 otherwise; x 1 if quarter 3, 0 otherwise 7.667-x₁-5x₂-2x3 X

(b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to three decimal places.) x₁ - 1 if quarter 1, 0 otherwise; x₂-1 if quarter 2, 0 otherwise; x 1 if quarter 3, 0 otherwise 7.667-x₁-5x₂-2x3 X

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 88CR
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Consider the following time series data. Quarter Year 1 1 2 3 4 ŷt= 3 1 4 6 Year 2 5 2 6 8 8.92 10.92 Year 3 6 5 (a) Construct a time series plot. What type of pattern exists in the data? O The time series plot shows a horizontal pattern, but there is also a seasonal pattern in the data. X 7 The time series plot shows a horizontal pattern and no seasonal pattern in the data. O The time series plot shows a linear trend and no seasonal pattern in the data. O The time series plot shows a linear trend and a seasonal pattern in the data. 9 (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to three decimal places.) X1 = 1 if quarter 1, 0 otherwise; X₂ = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise 7.667x₁5x₂2x3 (c) Compute the quarterly forecasts for the next year based on the model you developed in part (b). (Round your answers to two decimal places.) X quarter 1 forecast 6.67 2.67 quarter 2 forecast quarter 3 forecast quarter 4 forecast 5.67 7.67 (d) 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 (b) to capture seasonal effects and create a variable t such that t = 1 for quarter 1 in year 1, t = 2 for quarter 2 in year 1, ... t = 12 for quarter 4 in year 3. (Round your numerical values to three decimal places.) .417 +0.219x₁ - 4.188x2 — 1.594x3 +0.406 X (e) Compute the quarterly forecasts for the next year based on the model you developed in part (d). (Round your answers to two decimal places.) quarter 1 forecast 9.92 quarter 2 forecast 5.92 quarter 3 forecast quarter 4 forecast
Transcribed Image Text:Consider the following time series data. Quarter Year 1 1 2 3 4 ŷt= 3 1 4 6 Year 2 5 2 6 8 8.92 10.92 Year 3 6 5 (a) Construct a time series plot. What type of pattern exists in the data? O The time series plot shows a horizontal pattern, but there is also a seasonal pattern in the data. X 7 The time series plot shows a horizontal pattern and no seasonal pattern in the data. O The time series plot shows a linear trend and no seasonal pattern in the data. O The time series plot shows a linear trend and a seasonal pattern in the data. 9 (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to three decimal places.) X1 = 1 if quarter 1, 0 otherwise; X₂ = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise 7.667x₁5x₂2x3 (c) Compute the quarterly forecasts for the next year based on the model you developed in part (b). (Round your answers to two decimal places.) X quarter 1 forecast 6.67 2.67 quarter 2 forecast quarter 3 forecast quarter 4 forecast 5.67 7.67 (d) 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 (b) to capture seasonal effects and create a variable t such that t = 1 for quarter 1 in year 1, t = 2 for quarter 2 in year 1, ... t = 12 for quarter 4 in year 3. (Round your numerical values to three decimal places.) .417 +0.219x₁ - 4.188x2 — 1.594x3 +0.406 X (e) Compute the quarterly forecasts for the next year based on the model you developed in part (d). (Round your answers to two decimal places.) quarter 1 forecast 9.92 quarter 2 forecast 5.92 quarter 3 forecast quarter 4 forecast
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