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The image contains a problem related to linear and quadratic regression models for predicting weekly earnings. Let's break down the information:

### Given Data:
- **Year**: 2002, 2004, 2006, 2008, 2010
- **Weekly Earnings**: \$565, \$581, \$618, \$627, \$621

### Linear Regression Equation:
- $ y = 7.9x + 555 $
- Question: "What is the median weekly earnings for 2015 predicted by the linear regression equation?"
  - Answer: \$674 (rounded to the nearest dollar).

### Quadratic Regression Equation:
- $ y = -1.286x^2 + 23.329x + 519 $
- Question: "What is the median weekly earnings for 2015 predicted by the quadratic regression equation?"
  - To solve this, we need to plug in the value for $ x = 15 $ (since $ x $ represents the number of years since 2000 for 2015).

Let's calculate that prediction.The predicted median weekly earnings for 2015 using the quadratic regression equation is \$580 (rounded to the nearest dollar).

Do you want any additional details or have any questions about this? 

Here are five related questions to expand your understanding:
1. How do you interpret the coefficients in the quadratic regression equation?
2. How would the predicted value change if the trend for earnings fluctuates significantly in 2016 and beyond?
3. What are the limitations of using a quadratic model for long-term predictions?
4. How does the linear regression compare in accuracy to the quadratic regression for other years?
5. Can a cubic regression provide a better fit for this data set?

**Tip**: When using regression models, always assess the goodness of fit (like $R^2$) to evaluate how well the model represents the data.

The table below shows the median weekly earnings of a certain population of workers. Predict the median weekly earnings in 2015 using both a linear and a quadratic regression equation. Let x be the number of years since 2000 and y be the weekly earnings in dollars.

Learn how to predict median weekly earnings using linear and quadratic regression models. This problem covers essential algebraic concepts and is suitable for students in Grades 10-12. The example includes predictions for 2015 using both a linear equation (y = 7.9x + 555) and a quadratic equation (y = -1.286x^2 + 23.329x + 519).

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