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The image shows a table with the median weekly earnings for a population of workers in various years (2002, 2004, 2006, 2008, 2010), followed by tasks asking to predict the earnings for 2016 using both linear and quadratic regression models.

Here's how we can break down the tasks:

1. **Linear Regression Equation**:
   The linear regression equation is given as:

   \[
   y = 6.75x + 559.3
   \]

   Where $x$ is the number of years since 2000, and $y$ is the weekly earnings in dollars.

2. **Prediction for 2016 using Linear Regression**:
   For 2016, $x = 16$ (since $2016 - 2000 = 16$).

   Substitute $x = 16$ into the equation to find the predicted earnings:
   \[
   y = 6.75(16) + 559.3
   \]
   Let me calculate that.

I'll compute the result for the linear regression and explain how to approach the quadratic regression next.For the year 2016, the median weekly earnings predicted by the linear regression equation is approximately **$667** (rounded to the nearest dollar).

### Next Steps: Quadratic Regression
The quadratic regression equation isn't provided in the image. If you'd like, I can assist in developing the quadratic equation from the data points (years 2002, 2004, 2006, 2008, 2010 and their corresponding earnings).

Would you like help with that?

Here are 5 related questions you could explore:
1. How is a quadratic regression model different from a linear regression model?
2. Why would a quadratic regression sometimes give a better prediction for data trends?
3. How do we calculate the parameters for a quadratic regression equation?
4. What are the strengths and limitations of using regression models for predictions?
5. Can we compare the accuracy of both models using past data?

**Tip**: When fitting a quadratic model, look for patterns such as changes in the rate of increase or decrease in the data to determine if it's a better fit than a linear model.

The table below shows the median weekly earnings of a certain population of workers. If this trend continues, predict the median weekly earnings in 2016. Find both a linear and a quadratic regression equation to predict earnings.

Predict the median weekly earnings in 2016 using both linear and quadratic regression models based on data from 2002 to 2010. Learn how to apply regression techniques and understand their significance for predicting trends. Suitable for high school students studying algebra and statistics.

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