MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Table of Quarterly Sales of the TRK-50 Mountain Bike** The table below presents the quarterly sales of the TRK-50 mountain bike over four years by a bicycle shop in Switzerland. | Year | Quarter | \( t \) | \( y_t \) | |------|---------|---------|---------| | 1 | 1 | 1 | 10 | | 1 | 2 | 2 | 31 | | 1 | 3 | 3 | 43 | | 1 | 4 | 4 | 16 | | 2 | 1 | 5 | 11 | | 2 | 2 | 6 | 33 | | 2 | 3 | 7 | 45 | | 2 | 4 | 8 | 17 | | 3 | 1 | 9 | 13 | | 3 | 2 | 10 | 34 | | 3 | 3 | 11 | 48 | | 3 | 4 | 12 | 19 | | 4 | 1 | 13 | 15 | | 4 | 2 | 14 | 37 | | 4 | 3 | 15 | 51 | | 4 | 4 | 16 | 21 | ### Questions: (a) **Plot the Time Series:** - Use any statistical or graphing software to create a time series plot of \( y_t \) over \( t \). (b) **Trend Analysis:** - Examine the time series plot to determine the type of trend present. (c) **Seasonal Variation:** - Analyze the data to identify any seasonal patterns. (d) **Transformation for Constant Variation:** - Consider and discuss if data transformation is necessary. (e) **Fit a Model:** - Develop a model incorporating trend and seasonal variation terms. (f) **Importance of Variables:** - Assess and provide statistical evidence for the significance of the independent variables. (g) **Define Dummy Variables:** - Define dummy variables for quarters Q2, Q3, and
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Transcribed Image Text:**Table of Quarterly Sales of the TRK-50 Mountain Bike** The table below presents the quarterly sales of the TRK-50 mountain bike over four years by a bicycle shop in Switzerland. | Year | Quarter | \( t \) | \( y_t \) | |------|---------|---------|---------| | 1 | 1 | 1 | 10 | | 1 | 2 | 2 | 31 | | 1 | 3 | 3 | 43 | | 1 | 4 | 4 | 16 | | 2 | 1 | 5 | 11 | | 2 | 2 | 6 | 33 | | 2 | 3 | 7 | 45 | | 2 | 4 | 8 | 17 | | 3 | 1 | 9 | 13 | | 3 | 2 | 10 | 34 | | 3 | 3 | 11 | 48 | | 3 | 4 | 12 | 19 | | 4 | 1 | 13 | 15 | | 4 | 2 | 14 | 37 | | 4 | 3 | 15 | 51 | | 4 | 4 | 16 | 21 | ### Questions: (a) **Plot the Time Series:** - Use any statistical or graphing software to create a time series plot of \( y_t \) over \( t \). (b) **Trend Analysis:** - Examine the time series plot to determine the type of trend present. (c) **Seasonal Variation:** - Analyze the data to identify any seasonal patterns. (d) **Transformation for Constant Variation:** - Consider and discuss if data transformation is necessary. (e) **Fit a Model:** - Develop a model incorporating trend and seasonal variation terms. (f) **Importance of Variables:** - Assess and provide statistical evidence for the significance of the independent variables. (g) **Define Dummy Variables:** - Define dummy variables for quarters Q2, Q3, and
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