Given the linear regression equation for the median weekly earnings:

$y = 6.65x + 560.5$

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

To predict the earnings in the year 2016, first calculate $x$ for the year 2016:

$x = 2016 - 2000 = 16$

Now, substitute $x = 16$ into the linear regression equation:

$y = 6.65(16) + 560.5$

Calculating this:

$y = 106.4 + 560.5 = 666.9$

So, the predicted median weekly earnings for the year 2016 using the linear regression equation is approximately $666.9.

Would you like to calculate the quadratic regression next, or need any clarification?

Here are five questions to deepen the understanding of the concept:

1. How is a linear regression equation different from a quadratic regression equation?
2. What does the slope (6.65) represent in this linear regression equation?
3. How would predictions differ if a non-linear pattern was observed in the data?
4. What factors could cause deviations from the predicted earnings in real-world scenarios?
5. Can this regression model be used to predict earnings for a year far in the future, like 2050?

Tip: Always check the residuals (errors) after fitting a regression model to ensure that it is appropriate for the data!