Question

# The​ least-squares regression equation is ModifyingAbove y with caretyequals=731.9731.9xplus+14 comma 71114,711 where y is the median...

The​ least-squares regression equation is

ModifyingAbove y with caretyequals=731.9731.9xplus+14 comma 71114,711

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

0.76930.7693.

Complete parts​(a) through​ (d).

Bachelor's %Median Income

A scatter diagram has a horizontal axis labeled Bachelor's % from 15 to 60 in increments of 5 and a vertical axis labeled Median Income from 20000 to 55000 in increments of 5000. Points are scattered around a line that rises from left to right and has a slope of about 700.​(a) Predict the median income of a region in which

2020​%

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,

28.428.4

percent of adults 25 years and older have at least a​ bachelor's degree. The median income in this region is

​\$38 comma 74038,740.

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 every percent increase in adults having at least a​ bachelor's degree, the median income increases by

​\$nothing​,

on average.

B.For every dollar increase in median​ income, the percent of adults having at least a​ bachelor's degree is

nothing​%,

on average.

C.For​ 0% of adults having a​ bachelor's degree, the median income is predicted to be

​\$nothing.

D.For a median income of​ \$0, the percent of adults with a​ bachelor's degree is

nothing​%.

​(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 an​ x-value of 0 is outside the scope of the model.

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 a​ y-value of 0 does not make sense.

A)The median income of a region in which 20​%of adults 25 years and older have at least a​ bachelor's degree is 14711+731.9(20)= \$ 29,349

B)In a particular​ region,28.4 percent of adults 25 years and older have at least a​ bachelor's degree. The median income in this region is​ \$38,740.This income is higher than expected because the expected income is \$ 35,450.

C)The slope is interpreted as A.For every percent increase in adults having at least a​ bachelor's degree, the median income increases by \$731.9

D)B. It does not make sense to interpret the​ y-intercept because an​ x-value of 0 does not make sense.

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