The number of users of a certain website (in millions) from 2004 through 2011 follows. Year Period Users (Millions) 2004 1 1 2005 2 2006 11 2007 4 59 2008 146 2009 6 359 2010 608 2011 845 (a) Construct a time series plot. 900 900- 900 90 800 800 800 80 700 700 700 70 600- 600 500 600 60 500 500 50 400 400 400 40 300 300 300 30 200 200 llions of Users lions of Users Ilions of Users llions of Users

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# Analysis of Website User Growth from 2004 to 2011

The data presented in the table below shows the number of users (in millions) of a certain website over a span of eight years, from 2004 through 2011.

| Year | Period | Users (Millions) |
|------|--------|------------------|
| 2004 | 1      | 1                |
| 2005 | 2      | 6                |
| 2006 | 3      | 11               |
| 2007 | 4      | 59               |
| 2008 | 5      | 146              |
| 2009 | 6      | 359              |
| 2010 | 7      | 608              |
| 2011 | 8      | 845              |

### (a) Construct a Time Series Plot

The diagrams provided below illustrate different types of time series plots that represent user growth over the periods.

1. **Graph 1**: Depicts a downward linear trend.
2. **Graph 2**: Shows an upward linear trend.
3. **Graph 3**: Indicates a downward curvilinear trend.
4. **Graph 4**: Displays an upward curvilinear trend.

The accurate representation of the data should match the significant increase in users over time.

### Identifying Patterns

**Question:** What type of pattern exists?
- The time series plot exhibits a downward curvilinear trend.
- The time series plot exhibits an upward linear trend.
- The time series plot exhibits a downward linear trend.
- The time series plot exhibits an upward curvilinear trend.

The correct pattern based on the data provided is an upward curvilinear trend.

### (b) Forecasting Users

Using Minitab or Excel, develop a quadratic trend equation to forecast users (in millions). Round numerical values to one decimal place.

\[ T_t = \]

Enter the derived quadratic equation here. This equation will help predict future user numbers based upon the historical data trends observed.
Transcribed Image Text:# Analysis of Website User Growth from 2004 to 2011 The data presented in the table below shows the number of users (in millions) of a certain website over a span of eight years, from 2004 through 2011. | Year | Period | Users (Millions) | |------|--------|------------------| | 2004 | 1 | 1 | | 2005 | 2 | 6 | | 2006 | 3 | 11 | | 2007 | 4 | 59 | | 2008 | 5 | 146 | | 2009 | 6 | 359 | | 2010 | 7 | 608 | | 2011 | 8 | 845 | ### (a) Construct a Time Series Plot The diagrams provided below illustrate different types of time series plots that represent user growth over the periods. 1. **Graph 1**: Depicts a downward linear trend. 2. **Graph 2**: Shows an upward linear trend. 3. **Graph 3**: Indicates a downward curvilinear trend. 4. **Graph 4**: Displays an upward curvilinear trend. The accurate representation of the data should match the significant increase in users over time. ### Identifying Patterns **Question:** What type of pattern exists? - The time series plot exhibits a downward curvilinear trend. - The time series plot exhibits an upward linear trend. - The time series plot exhibits a downward linear trend. - The time series plot exhibits an upward curvilinear trend. The correct pattern based on the data provided is an upward curvilinear trend. ### (b) Forecasting Users Using Minitab or Excel, develop a quadratic trend equation to forecast users (in millions). Round numerical values to one decimal place. \[ T_t = \] Enter the derived quadratic equation here. This equation will help predict future user numbers based upon the historical data trends observed.
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