Question

The​ least-squares regression equation is ModifyingAbove y with caretequals653.1xplus16 comma 240 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 0.7245. 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. ​$ nothing ​(Round to the nearest dollar as​ needed.) ​

(b) In a particular​ region, 29.1 percent of adults 25 years and older have at least a​ bachelor's degree. The median income in this region is ​$38 comma 463. Is this income higher than what you would​ expect? Why? This is ▼ higher lower than expected because the expected income is ​$ nothing ​(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.) A. For a median income of​ $0, the percent of adults with a​ bachelor's degree is nothing​%. B. For​ 0% of adults having a​ bachelor's degree, the median income is predicted to be ​$ nothing. C. For every dollar increase in median​ income, the percent of adults having at least a​ bachelor's degree is nothing​%, on average. D. For every percent increase in adults having at least a​ bachelor's degree, the median income increases by ​$ nothing​, on average. ​

(d) Explain why it does not make sense to interpret the​ y-intercept. Choose the correct answer below. A. It does not make sense to interpret the​ y-intercept because a​ y-value of 0 does not make sense. B. It does not make sense to interpret the​ y-intercept because an​ x-value of 0 does not make sense. C. It does not make sense to interpret the​ y-intercept because a​ y-value of 0 is outside the scope of the model. D. It does not make sense to interpret the​ y-intercept because an​ x-value of 0 is outside the scope of the model.

Answer 1

The least squares regression equation is:

y = 653.1x + 16240

a) When x = 20
y = 653.1*20 + 16240 = $29302

b) When x = 29.1%
y = 653.1*29.1 + 16240 = $35245 (expected) (rounded off to the nearest dollar)
Actual Median income in the region = $38463

This is higher than expected because the expected income is $35245

c) Correct Option: D) For every percent increase in adults having at least a​ bachelor's degree, the median income increases by ​$653.1, on average. ​

d) The intercept is the y-value when x-value 0. It is outside the scope of the model.
D) is correct