The table below shows the median weekly earnings of a certain population of workers. If this trend​ continues, predict the median weekly earnings in 2015. For this​ exercise, find a linear and a quadratic regression equation and use both to predict the earnings in 2015. Let x be the number of years since the year 2000 and y be the weekly earnings in dollars.Year	Weekly Earnings (in dollars)			
2002	575			
2004	581			
2006	619			
2008	626			
2010	620			

To solve this problem and predict the median weekly earnings in 2015 using both linear and quadratic regression equations, we will follow these steps:

### 1. Organize the dataTo solve this problem and predict the median weekly earnings in 2015 using both linear and quadratic regression equations, we will follow these steps:

### 1. Organize the 
We are given the year and corresponding weekly earnings. To make this work in terms of the variable $ x $ (years since 2000), we convert the years into $ x $ values:
- 2002 corresponds to $ x = 2 $
- 2004 corresponds to $ x = 4 $
- 2006 corresponds to $ x = 6 $
- 2008 corresponds to $ x = 8 $
- 2010 corresponds to $ x = 10 $

This gives us the following data points:
\[
(2, 575), (4, 581), (6, 619), (8, 626), (10, 620)
\]

### 2. Linear Regression Equation:

A linear regression equation has the form:
\[
y = ax + b
\]
where $ a $ is the slope and $ b $ is the y-intercept. We can calculate these values using linear regression formulas or a calculator.

### 3. Quadratic Regression Equation:

A quadratic regression equation has the form:
\[
y = ax^2 + bx + c
\]
where $ a $, $ b $, and $ c $ are constants determined through regression.

### 4. Predictions for 2015:

For both equations, we will substitute $ x = 15 $ (since 2015 is 15 years after 2000) to predict the weekly earnings.

I'll calculate the regression equations and predict the value of weekly earnings using both models.### 1. Linear Regression Equation:
The linear regression equation is:
\[
y = 6.75x + 563.7
\]
Using this equation to predict the weekly earnings in 2015 ($x = 15$):
\[
y = 6.75(15) + 563.7 = 664.95
\]
Thus, the predicted earnings in 2015 using the linear model is **$664.95**.

### 2. Quadratic Regression Equation:
The quadratic regression equation is:
\[
y = -0.982x^2 + 18.536x + 536.2
\]
Using this equation to predict the weekly earnings in 2015 ($x = 15$):
\[
y = -0.982(15)^2 + 18.536(15) + 536.2 = 593.25
\]
Thus, the predicted earnings in 2015 using the quadratic model is **$593.25**.

### Summary:
- **Linear model prediction for 2015:** $664.95
- **Quadratic model prediction for 2015:** $593.25

Would you like more details on these results or any specific part of the calculations?

Here are five related questions to deepen your understanding:
1. What factors might make the quadratic regression more accurate than the linear regression?
2. How would increasing the number of data points improve the accuracy of regression predictions?
3. Can regression models be used to predict other types of financial data, such as inflation?
4. How does the quadratic term affect the curve of the quadratic regression?
5. What is the correlation coefficient of the linear regression, and how does it measure fit?

**Tip:** The accuracy of regression models can often be tested by calculating the "residuals," which are the differences between actual data points and the model's predicted values.

The table below shows the median weekly earnings of a certain population of workers. If this trend​ continues, predict the median weekly earnings in 2015. For this​ exercise, find a linear and a quadratic regression equation and use both to predict the earnings in 2015. Let x be the number of years since the year 2000 and y be the weekly earnings in dollars.Year Weekly Earnings (in dollars) 2002 575 2004 581 2006 619 2008 626 2010 620.

Learn how to predict the median weekly earnings in 2015 using linear and quadratic regression. This problem provides data from 2002 to 2010 and explains how to apply algebraic and statistical concepts, including linear and quadratic equations. Suitable for students in Grades 10-12.

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