Let X be a random variable representing the number of years of education an individual has,...

Let X be a random variable representing the number of years of education an individual has, and let Y be a random variable representing an individual’s annual income. Suppose that the latest research in economics has concluded that:

Y = 6X +U

(1)

is the correct model for the relationship between X and Y , where U is another random variable that is independent of X. Suppose Var(X) = 2 and Var(Y ) = 172.

a. Find Var(U).

b. Find Cov(X, Y ) and corr(X, Y ).

c. The variance in Y (income) comes from variance in X (education) and U (other factors unobserved to us). What fraction of the variance in income is explained by variance in education?

d. How does the fraction you found in (c) compare to corr(Y, X)?

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Expert Solution

milcah answered 9 months ago

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