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 ŷ = 703.5x + 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 intercept.

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Percent of Population with At Least a Bachelor's Degree vs. Median Income 55000 50000 45000 40000 35000 30000 50 Bachelors % Median Income