NW 13. Income and Education In Problem 15 from Section 4.1, a scatter diagram an
ID: 3370690 • Letter: N
Question
NW 13. Income and Education In Problem 15 from Section 4.1, a scatter diagram and correlation coefficient suggested there is a linear relation between the percentage of individuals who have at least a bachelor's degree and median income in the states. In fact, the least-squares regression equation is y = 7035x + 14.920 where y is the median income and x is the percentage of individuals 25 years and older with at least a bachelor's degree in the state (a) Predict the median income of a state in which 25% of adults 25 years and older have at least a bachelor's degree. (b) In North Dakota, 27.1 percent of adults 25 years and older have at least a bachelor's degree. The median income in North Dakota is $37,193. Is this income higher than what you would expect? Why? (c) Interpret the slope. (d) Explain why it does not make sense to interpret the interceptExplanation / Answer
a) The predict the median income of a state in which 25% of adult 25 years and older is
Y-hat = 703.5 (25) + 14920 = 32507.5
b) The predict the median income of a state in which 27.1% of adult 25 years and older is
Y-hat = 703.5 (27.1) + 14920 = 33984.85
Given North Dakota income is $37193
Yes, this income is higher than what y would expect.
since North Dakota income is $37193 is higher than y-hat = 33984.85
c) Slope = 703.5 > 0 so it is positive correlation between median income and percentage of individuals 25 years and older
As the indivual 25 years and older increase 1 percentage then median income will be increase $703.5
d) Intercept = 14920
If the percentage of indivual 25 years and older is zero (i.e. x= 0 ) then Y-hat i.e. median income is 14920
which is meaning less.
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