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The following table shows a company's annual revenue (in billions of dollars) for 2009 to 2014. Period (t) Revenue ($ billions) Year 2009 2010 2011 2012 2013 2014 80- 70- 1 (a) Construct a time series plot. 0 2 1 5 6 2 DENK 5 6 3 23.8 Period 29.2 37.9 50.2 59.7 66.8 ⓇO 0 1 2 Period 1 2 Period 5 6 no 20 10- 0 1 2 3 Period. Ⓡ

The following table shows a company's annual revenue (in billions of dollars) for 2009 to 2014. Period (t) Revenue ($ billions) Year 2009 2010 2011 2012 2013 2014 80- 70- 1 (a) Construct a time series plot. 0 2 1 5 6 2 DENK 5 6 3 23.8 Period 29.2 37.9 50.2 59.7 66.8 ⓇO 0 1 2 Period 1 2 Period 5 6 no 20 10- 0 1 2 3 Period. Ⓡ

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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### Analyzing Time Series Data for Revenue Forecasting #### Question (a) **What type of pattern exists in the data?** - The time series plot shows an upward linear trend. - The time series plot shows an upward curvilinear trend. - The time series plot shows a downward linear trend. - The time series plot shows a downward curvilinear trend. #### Question (b) **Develop a linear trend equation for this time series to forecast revenue (in billions of dollars).** (Round your numerical values to three decimal places.) \[ T_t = \text{____} \] #### Question (c) **What is the average revenue increase per year (in billions of dollars) that this company has been realizing?** (Round your answer to three decimal places.) \[ \$ \text{____} \text{ billion} \] #### Question (d) **Compute an estimate of this company's revenue (in billions of dollars) for 2015.** (Round your answer to two decimal places.) \[ \$ \text{____} \text{ billion} \] --- These exercises guide you through identifying patterns in time series data, developing a trend equation, and calculating both average annual revenue increases and future revenue estimates. Use the options, provided data, and rounding instructions carefully to ensure accurate and meaningful results.
Transcribed Image Text:### Analyzing Time Series Data for Revenue Forecasting #### Question (a) **What type of pattern exists in the data?** - The time series plot shows an upward linear trend. - The time series plot shows an upward curvilinear trend. - The time series plot shows a downward linear trend. - The time series plot shows a downward curvilinear trend. #### Question (b) **Develop a linear trend equation for this time series to forecast revenue (in billions of dollars).** (Round your numerical values to three decimal places.) \[ T_t = \text{____} \] #### Question (c) **What is the average revenue increase per year (in billions of dollars) that this company has been realizing?** (Round your answer to three decimal places.) \[ \$ \text{____} \text{ billion} \] #### Question (d) **Compute an estimate of this company's revenue (in billions of dollars) for 2015.** (Round your answer to two decimal places.) \[ \$ \text{____} \text{ billion} \] --- These exercises guide you through identifying patterns in time series data, developing a trend equation, and calculating both average annual revenue increases and future revenue estimates. Use the options, provided data, and rounding instructions carefully to ensure accurate and meaningful results.
### Annual Revenue Analysis from 2009 to 2014 #### Table Overview The following table presents a company's annual revenue (in billions of dollars) for the years 2009 to 2014: | Year | Period (t) | Revenue ($ billions) | |------|------------|----------------------| | 2009 | 1 | 23.8 | | 2010 | 2 | 29.2 | | 2011 | 3 | 37.9 | | 2012 | 4 | 50.2 | | 2013 | 5 | 59.7 | | 2014 | 6 | 66.8 | #### Graphical Representation (a) **Constructing a Time Series Plot** Four different time series plots are provided below: 1. **First Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: The graph shows an impressive initial increase in revenue, peaking just above 50 billion dollars around period 4, followed by a noticeable decline after period 5. 2. **Second Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: The revenue decreases initially, reaching a trough at period 3, but then continues to rise steadily from periods 4 to 6. 3. **Third Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: This graph suggests a steady decline in revenue across all periods, with revenue starting at around 66.8 billion dollars and gradually reducing to about 23.8 billion dollars. 4. **Fourth Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: This graph represents a constant and direct increase in revenue over time, starting from 23.8 billion
Transcribed Image Text:### Annual Revenue Analysis from 2009 to 2014 #### Table Overview The following table presents a company's annual revenue (in billions of dollars) for the years 2009 to 2014: | Year | Period (t) | Revenue ($ billions) | |------|------------|----------------------| | 2009 | 1 | 23.8 | | 2010 | 2 | 29.2 | | 2011 | 3 | 37.9 | | 2012 | 4 | 50.2 | | 2013 | 5 | 59.7 | | 2014 | 6 | 66.8 | #### Graphical Representation (a) **Constructing a Time Series Plot** Four different time series plots are provided below: 1. **First Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: The graph shows an impressive initial increase in revenue, peaking just above 50 billion dollars around period 4, followed by a noticeable decline after period 5. 2. **Second Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: The revenue decreases initially, reaching a trough at period 3, but then continues to rise steadily from periods 4 to 6. 3. **Third Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: This graph suggests a steady decline in revenue across all periods, with revenue starting at around 66.8 billion dollars and gradually reducing to about 23.8 billion dollars. 4. **Fourth Plot:** - **X-axis**: Period (t) ranging from 0 to 7. - **Y-axis**: Revenue ($ billions) ranging from 0 to 80. - **Data Points**: This graph represents a constant and direct increase in revenue over time, starting from 23.8 billion
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