The table below shows the median weekly earnings of a certain population of workers. If this trend​ continues, predict the median weekly earnings in 201616. For this​ exercise, find a linear and a quadratic regression equation and use both to predict the earnings in 201616. Let x be the number of years since the year 2000 and y be the weekly earnings in dollars.
Year
2002
2004
2006
2008
2010

Weekly Earnings
​(in dollars)
570570
580580
613613
625625
614614
Question content area bottom
Part 1
A linear regression equation is yequals=6.65 x plus 560.56.65x+560.5.
​(Use integers or decimals for any numbers in the equation. Round to three decimal places as​ needed.)
Part 2
What is the median weekly earnings for 201616 predicted by the linear regression​ equation?

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!

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. For this exercise, find a linear and a quadratic regression equation and use both to predict the earnings in 2016. Let x be the number of years since the year 2000 and y be the weekly earnings in dollars.
Year
2002
2004
2006
2008
2010
Weekly Earnings (in dollars)
570
580
613
625
614

Part 1: A linear regression equation is y = 6.65x + 560.5. Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.

Part 2: What is the median weekly earnings for 2016 predicted by the linear regression equation?

Learn how to predict the median weekly earnings of workers using linear and quadratic regression models. This problem uses historical data from 2000 to 2010 to forecast earnings for the year 2016. Understand key concepts such as linear regression equations and the least squares method, perfect for students in Grades 10-12.

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