Question: Here are data on the years of schooling completed, x, and annual income, y, (in thousands of dollars), for a sample of 18-40 year old men.

Years 10 16 12 6 12 12 16 16 18

Income 28 38 16 13 25 30 35 27 28

Years 12 10 12 16 14 11 12 19 16

Income 28 26 21 34 30 21 27 29 24

A scatter plot (don’t do it) shows a generally linear relation, but with considerable scatter about the line of best fit. A computer least-squares regression program gives the output shown. (The “Coef” column gives the intercept a and slope b; the “Std Error” column gives the standard errors of these statistics. The “Residual Standard Error” is the observed standard deviation s about the regression line.

Coef Std Error t Value

Intercept 10.84249 5.103363 2.124577

X2 1.186813 0.372311 3.187693

Residual standard error= 5.02275 R-Square= 0.3884116

N= 18 F Value = 10.16139 on 1, 16 df

a. What percent of observed variation in income is explained by the straight-line relation between incoMeand education?

b. Is there strong evidence that there is a straight-line relation between education and income (state hypotheses, carry out a test, use a table to find values between which the P-value falls, and state your conclusion.

c. Consider 40 year old men who have 16 years of education. These are men with four years of college but no further education.) Give a 95% confidence interval for their average income.