Consider a simple regression in which the dependent variable MIM mean income of males who are 18 years of age or older, in thousands

Consider a simple regression in which the dependent variable MIM ¼ mean income of males who are 18 years of age or older, in thousands of dollars. The explanatory variable PMHS ¼ percent of males 18 or older who are high school graduates. The data consist of 51 observations on the 50 states plus the District of Columbia. Thus MIM and PMHS are ‘‘state averages.’’ The estimated regression, along with standard errors and t-statistics, is MIM b ¼ ðaÞ þ 0:180PMHS

ðseÞ ð2:174Þ ðbÞ

ðtÞ ð1:257Þ ð5:754Þ

(a) What is the estimated equation intercept? Show your calculation. Sketch the estimated regression function.

(b) What is the standard error of the estimated slope? Show your calculation.

(c) What is the p-value for the two-tail test of the hypothesis that the equation intercept is zero? Draw a sketch to illustrate.

(d) State the economic interpretation of the estimated slope. Is the sign of the coefficient what you would expect from economic theory?

(e) Construct a 99% confidence interval estimate of the slope of this relationship.

(f) Test the hypothesis that the slope of the relationship is 0.2 against the alternative that it is not. State in words the meaning of the null hypothesis in the context of this problem.