Recall Duncan’s regression of occupational prestige on the educational and income levels of occupations. Following Duncan, regress prestige on education and income.

Also, perform a simple regression of prestige on income alone. Then add random measurement errors to education. Sample these measurement errors from a normal distribution with mean 0, repeating the exercise for each of the following measurement error variances: σ2

δ¼ 102, 252, 502, 1002. In each case, recompute the regression of prestige on income and education. Then, treating the initial multiple regression as corresponding to σ2

δ ¼ 0, plot the coefficients of education and income as a function of σ2

δ . What happens to the education coefficient as measurement error in education grows? What happens to the income coefficient?