The table below shows the number of millions of internet users in a particular region. Let x represent the number of years since 2000. a. Write a linear regression equation for this data. b. Write a quadratic regression equation for this data. c. Use each regression equation to predict the number of internet users in the year 2011. Year 2001 2003 Number of users (in millions) 174 213 2000 145 2002 200 2004 233 2005 244 2006 263 2007 286
The table below shows the number of millions of internet users in a particular region. Let x represent the number of years since 2000. a. Write a linear regression equation for this data. b. Write a quadratic regression equation for this data. c. Use each regression equation to predict the number of internet users in the year 2011. Year 2001 2003 Number of users (in millions) 174 213 2000 145 2002 200 2004 233 2005 244 2006 263 2007 286
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Internet Usage Growth Over Time
The table below shows the number of millions of internet users in a particular region, recorded annually. In this dataset, \( x \) represents the number of years since the year 2000. This data will be used to write and analyze both linear and quadratic regression equations to understand the growth pattern of internet users over this period. Predictions will also be made for future internet usage based on these patterns.
| Year | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 |
|------|------|------|------|------|------|------|------|------|
| Number of Users (in millions) | 145 | 174 | 200 | 213 | 233 | 244 | 263 | 286 |
#### Tasks:
1. **Linear Regression Equation:**
- Write a linear regression equation for this data.
2. **Quadratic Regression Equation:**
- Write a quadratic regression equation for this data.
3. **Prediction for Year 2011:**
- Use each regression equation to predict the number of internet users in the year 2011.
#### Graph Analysis:
No specific graphs or diagrams are provided in this data table; however, visualizing the data points on a scatter plot and fitting the corresponding regression lines (linear and quadratic) can aid in better understanding the growth trends.
### Linear Regression
To create a linear regression equation, we assume the relationship between year and number of users is linear. The general form of a linear equation is:
\[ y = mx + b \]
Where \( y \) is the number of users, \( x \) is the number of years since 2000, \( m \) is the slope, and \( b \) is the y-intercept.
### Quadratic Regression
For quadratic regression, we assume there is a non-linear relationship. The general form of a quadratic equation is:
\[ y = ax^2 + bx + c \]
Where \( y \) is the number of users, \( x \) is the number of years since 2000, and \( a \), \( b \), and \( c \) are coefficients that need to be determined.
### Prediction for Year 2011
Once the equations are formulated:
- For linear regression, set \( x = 11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2a881fc-0749-48b7-aba0-5bec7959e8c8%2F56f19ea1-7359-4708-a91e-57d85cdfde6d%2Fqdr4qgr_processed.png&w=3840&q=75)
Transcribed Image Text:### Internet Usage Growth Over Time
The table below shows the number of millions of internet users in a particular region, recorded annually. In this dataset, \( x \) represents the number of years since the year 2000. This data will be used to write and analyze both linear and quadratic regression equations to understand the growth pattern of internet users over this period. Predictions will also be made for future internet usage based on these patterns.
| Year | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 |
|------|------|------|------|------|------|------|------|------|
| Number of Users (in millions) | 145 | 174 | 200 | 213 | 233 | 244 | 263 | 286 |
#### Tasks:
1. **Linear Regression Equation:**
- Write a linear regression equation for this data.
2. **Quadratic Regression Equation:**
- Write a quadratic regression equation for this data.
3. **Prediction for Year 2011:**
- Use each regression equation to predict the number of internet users in the year 2011.
#### Graph Analysis:
No specific graphs or diagrams are provided in this data table; however, visualizing the data points on a scatter plot and fitting the corresponding regression lines (linear and quadratic) can aid in better understanding the growth trends.
### Linear Regression
To create a linear regression equation, we assume the relationship between year and number of users is linear. The general form of a linear equation is:
\[ y = mx + b \]
Where \( y \) is the number of users, \( x \) is the number of years since 2000, \( m \) is the slope, and \( b \) is the y-intercept.
### Quadratic Regression
For quadratic regression, we assume there is a non-linear relationship. The general form of a quadratic equation is:
\[ y = ax^2 + bx + c \]
Where \( y \) is the number of users, \( x \) is the number of years since 2000, and \( a \), \( b \), and \( c \) are coefficients that need to be determined.
### Prediction for Year 2011
Once the equations are formulated:
- For linear regression, set \( x = 11
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