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Consider the following time series data. Quarter Year 1 Year 2 1 3 5 2 3 4 1 4 6 2 6 8 Year 3 6 5 7 9 (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 linear trend and a seasonal pattern in the data. The time series plot shows a horizontal pattern, but there is also a seasonal pattern 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. (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 (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.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast

Consider the following time series data. Quarter Year 1 Year 2 1 3 5 2 3 4 1 4 6 2 6 8 Year 3 6 5 7 9 (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 linear trend and a seasonal pattern in the data. The time series plot shows a horizontal pattern, but there is also a seasonal pattern 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. (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 (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.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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Consider the following time series data. Quarter Year 1 1 De- 2 3 4 3 1 4 6 Year 2 quarter 3 forecast quarter 4 forecast 5 2 6 8 Year 3 6 5 7 (a) Construct a time series plot. What type of pattern exists in the data? O 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. O The time series plot shows a linear trend and a seasonal pattern in the data. O The time series plot shows a horizontal pattern, but there is also 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; x₂ = 1 If quarter 3, 0 otherwise (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.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast (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.) &t= (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 quarter 2 forecast (f) Is the model you developed in part (b) or the model you developed in part (d) more effective? Justify your answer. O The model in part (b) appears to be more effective since there is no linear trend visible in the data. O The model in part (d) appears to be more effective since it has a lower MSE than the model in part (b). O The model in part (b) appears to be more effective since it has a lower MSE than the model in part (d). O The model in part (d) appears to be more effective since it has more variables than the model in part (b). O The model in part (b) appears to be more effective since it has a higher MSE than the model in part (d).
Transcribed Image Text:Consider the following time series data. Quarter Year 1 1 De- 2 3 4 3 1 4 6 Year 2 quarter 3 forecast quarter 4 forecast 5 2 6 8 Year 3 6 5 7 (a) Construct a time series plot. What type of pattern exists in the data? O 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. O The time series plot shows a linear trend and a seasonal pattern in the data. O The time series plot shows a horizontal pattern, but there is also 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; x₂ = 1 If quarter 3, 0 otherwise (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.) quarter 1 forecast quarter 2 forecast quarter 3 forecast quarter 4 forecast (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.) &t= (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 quarter 2 forecast (f) Is the model you developed in part (b) or the model you developed in part (d) more effective? Justify your answer. O The model in part (b) appears to be more effective since there is no linear trend visible in the data. O The model in part (d) appears to be more effective since it has a lower MSE than the model in part (b). O The model in part (b) appears to be more effective since it has a lower MSE than the model in part (d). O The model in part (d) appears to be more effective since it has more variables than the model in part (b). O The model in part (b) appears to be more effective since it has a higher MSE than the model in part (d).
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