The least-squares regression equation given is:

$\hat{y} = 556.7x + 18,553$

Where:

• $\hat{y}$ is the predicted median income,
• $x$ is the percentage of people 25 years and older with at least a bachelor's degree.

For part (a), we are asked to predict the median income when $x = 25\%$.

Substitute $x = 25$ into the equation:

$\hat{y} = 556.7(25) + 18,553$

First, calculate $556.7 \times 25$:

$556.7 \times 25 = 13,917.5$

Now add this to 18,553:

$\hat{y} = 13,917.5 + 18,553 = 32,470.5$

So, the predicted median income for a region where 25% of adults 25 years and older have at least a bachelor's degree is $32,470.50.

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Would you like further clarification on how I got the result or how to interpret the regression equation?

Here are some related questions to explore:

1. How does the slope of the regression equation affect the predicted income?
2. What is the significance of the correlation coefficient (0.7186) in this context?
3. How would the prediction change if the percentage of adults with at least a bachelor’s degree were 40%?
4. How would you use this regression model to estimate income for other education levels?
5. What is the meaning of the intercept value (18,553) in the regression equation?

Tip: The slope of the regression equation shows the amount by which the median income increases for every 1% increase in the percentage of people with at least a bachelor’s degree.