Questions: The least-squares regression equation is ŷ=775.8x+11,824 where y is the median income of a region and x is the percentage of adults 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8017. Complete parts (a) through (d). (a) Predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. 27,340 (Round to the nearest dollar as needed.) (b) In a particular region, 25.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is 35,076. Is this income higher than what you would expect? Why? This is than expected because the expected income is (Round to the nearest dollar as needed.)

The least-squares regression equation is ŷ=775.8x+11,824 where y is the median income of a region and x is the percentage of adults 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8017. Complete parts (a) through (d).
(a) Predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree.
27,340 (Round to the nearest dollar as needed.)
(b) In a particular region, 25.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is 35,076. Is this income higher than what you would expect? Why?

This is than expected because the expected income is
(Round to the nearest dollar as needed.)

Transcript text: The least-squares regression equation is $\hat{y}=775.8 x+11,824$ where $y$ is the median income of a region and $x$ is the percentage of adults 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8017 . Complete parts (a) through (d). (a) Predict the median income of a region in which $20 \%$ of adults 25 years and older have at least a bachelor's degree. $\$ 27,340$ (Round to the nearest dollar as needed.) (b) In a particular region, 25.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $\$ 35,076$. Is this income higher than what you would expect? Why? This is $\square$ than expected because the expected income is $\$$ $\square$ (Round to the nearest dollar as needed.)

Solution

Solution Steps

Step 1: Identify the given regression equation

The given least-squares regression equation is: \[ \hat{y} = 775.8x + 11,824 \] where $ y $ is the median income of a region and $ x $ is the percentage of adults 25 years and older with at least a bachelor's degree in the region.

Step 2: Substitute the given value into the regression equation

For part (a), we need to predict the median income when $ x = 20 \% $.

Step 3: Calculate the predicted median income

Substitute $ x = 20 $ into the regression equation: \[ \hat{y} = 775.8(20) + 11,824 \] \[ \hat{y} = 15,516 + 11,824 \] \[ \hat{y} = 27,340 \]