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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