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The quarterly sales of the TRK-50 mountain bike for the previous four years by a bicycle shop in Switzerland is presented in the following table. Year 1 2 3 Quarter 1 2 3 4 1 2 3 4 1 2 3 st 4 1 2 W|N 3 4 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Yt 10 31 43 16 11 33 45 17 13 34 48 19 15 37 51 21 (a) By using a software of your choice, plot the time series (b) What kind of trend appears to exist? (c) What type of seasonal variation appears to exist? (d) Is a transformation needed to obtain a series that displays constant variation? (e) Fit a proper model with trend and seasonal variations terms. (f) Do all the independent variables seem to be important? Justify your answer

The quarterly sales of the TRK-50 mountain bike for the previous four years by a bicycle shop in Switzerland is presented in the following table. Year 1 2 3 Quarter 1 2 3 4 1 2 3 4 1 2 3 st 4 1 2 W|N 3 4 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Yt 10 31 43 16 11 33 45 17 13 34 48 19 15 37 51 21 (a) By using a software of your choice, plot the time series (b) What kind of trend appears to exist? (c) What type of seasonal variation appears to exist? (d) Is a transformation needed to obtain a series that displays constant variation? (e) Fit a proper model with trend and seasonal variations terms. (f) Do all the independent variables seem to be important? Justify your answer

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Quarterly Sales Data of TRK-50 Mountain Bike** The following table represents the quarterly sales of the TRK-50 mountain bike over the previous four years at a bicycle shop in Switzerland. | Year | Quarter | \( t \) | \( y_t \) | |------|---------|---------|----------| | 1 | 1 | 1 | 10 | | | 2 | 2 | 31 | | | 3 | 3 | 43 | | | 4 | 4 | 16 | | 2 | 1 | 5 | 11 | | | 2 | 6 | 33 | | | 3 | 7 | 45 | | | 4 | 8 | 17 | | 3 | 1 | 9 | 13 | | | 2 | 10 | 34 | | | 3 | 11 | 48 | | | 4 | 12 | 19 | | 4 | 1 | 13 | 15 | | | 2 | 14 | 37 | | | 3 | 15 | 51 | | | 4 | 16 | 21 | **Discussion Questions:** (a) **Time Series Plot**: Using software tools, plot the time series data to visualize trends and seasonal patterns. (b) **Trend Analysis**: Determine the nature of the trend in sales over the time period. (c) **Seasonal Variation**: Identify the type of seasonal variation present in the data. (d) **Data Transformation**: Consider if a transformation is needed for constant variation in the series. (e) **Model Fitting**: Fit a suitable model that includes both trend and seasonal variations. (f) **Variable Importance**: Analyze the importance of the independent variables statistically. (g) **Dummy Variables**: Define the dummy variables Q2, Q3, and Q4 for quarterly effects. (h) **Sales Prediction**: Use the fitted model to predict bike sales in the fifth year, including point estimation and constructing a 95% confidence and prediction interval. (i) **Prediction Equation
Transcribed Image Text:**Quarterly Sales Data of TRK-50 Mountain Bike** The following table represents the quarterly sales of the TRK-50 mountain bike over the previous four years at a bicycle shop in Switzerland. | Year | Quarter | \( t \) | \( y_t \) | |------|---------|---------|----------| | 1 | 1 | 1 | 10 | | | 2 | 2 | 31 | | | 3 | 3 | 43 | | | 4 | 4 | 16 | | 2 | 1 | 5 | 11 | | | 2 | 6 | 33 | | | 3 | 7 | 45 | | | 4 | 8 | 17 | | 3 | 1 | 9 | 13 | | | 2 | 10 | 34 | | | 3 | 11 | 48 | | | 4 | 12 | 19 | | 4 | 1 | 13 | 15 | | | 2 | 14 | 37 | | | 3 | 15 | 51 | | | 4 | 16 | 21 | **Discussion Questions:** (a) **Time Series Plot**: Using software tools, plot the time series data to visualize trends and seasonal patterns. (b) **Trend Analysis**: Determine the nature of the trend in sales over the time period. (c) **Seasonal Variation**: Identify the type of seasonal variation present in the data. (d) **Data Transformation**: Consider if a transformation is needed for constant variation in the series. (e) **Model Fitting**: Fit a suitable model that includes both trend and seasonal variations. (f) **Variable Importance**: Analyze the importance of the independent variables statistically. (g) **Dummy Variables**: Define the dummy variables Q2, Q3, and Q4 for quarterly effects. (h) **Sales Prediction**: Use the fitted model to predict bike sales in the fifth year, including point estimation and constructing a 95% confidence and prediction interval. (i) **Prediction Equation
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