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...

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
δ= 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 = 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?