a. The predicted median income for this region is approximately $31,850.
b. Since the observed income ($36,704) is higher than $33,468.68 , we can conclude that it is higher than what was expected.
c. The correct interpretation of the slope is:
C. For every percent increase in adults having at least a bachelor's degree, the median income increases by $770.8, on average.
d. It does not make sense to interpret the y-intercept in this context because it represents the predicted median income when the percentage of adults with a bachelor's degree is 0%.
How to predict median income
(a) To predict the median income of a region where 25% of adults 25 years and older have at least a bachelor's degree,
substitute x = 25 into the regression equation:
y = 770.8x + 12,580
y = 770.8(25) + 12,580
y ≈ 31,850
Therefore, the predicted median income for this region is approximately $31,850.
(b) In the particular region where 27.1 percent of adults 25 years and older have at least a bachelor's degree, the observed median income is $36,704. To determine if this income is higher or lower than expected, we compare it to the predicted income using the regression equation:
y = 770.8x + 12,580
y = 770.8(27.1) + 12,580
y ≈ 33,468.68
The expected income, based on the regression equation, is approximately $33,468.68. Since the observed income ($36,704) is higher than $33,468.68 , we can conclude that it is higher than what was expected.
(c) The slope of the regression equation represents the average change in the median income for each one-unit increase in the percentage of adults with at least a bachelor's degree.
In this case, the slope is 770.8. So, for every 1% increase in the percentage of adults with a bachelor's degree, on average, the median income increases by $770.8.
Therefore, the correct interpretation of the slope is:
OC. For every percent increase in adults having at least a bachelor's degree, the median income increases by $770.8, on average.
(d) It does not make sense to interpret the y-intercept in this context because it represents the predicted median income when the percentage of adults with a bachelor's degree is 0%.
However, it is highly unlikely that a region would have 0% of adults with at least a bachelor's degree. Therefore, interpreting the y-intercept in this case is not meaningful or relevant to the given data.
Complete questions
The least-squares regression equation is y = 770.8x + 12,580 where y is the median income and x is the percentage of 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 0.7575. Complete parts (a) through (d). 15 20 25 30 35 40 45 50 55 60 Bachelor's % C (a) Predict the median income of a region in which 25% of adults 25 years and older have at least a bachelor's degree. $ (Round to the nearest dollar as needed.) (b) In a particular region, 27.1 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $36,704. 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.) (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do not round.) OA. For a median income of $0, the percent of adults with a bachelor's degree is %. OB. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is %, on average. OC. For every percent increase in adults having at least a bachelor's degree, the median income increases by $, on average. O D. For 0% of adults having a bachelor's degree, the median income is predicted to be $ (d) Explain why it does not make sense to interpret the y-intercept.