Calculate by hand a regression of the data for p on the data for e in Exercise 1.3, first using all 12 observations, then excluding the observation for Japan, and provide an economic interpretation.
Exercise 1.3
Using the data in Exercise 1.1, calculate Var(Y), Var(S), Var(T), and Cov(S, T) and verify that
Var(Y) = 250,000 Var(X) + 40,000 Var(T) + 200,000 Cov(S, T),
explaining analytically why this should be the case.
In a large bureaucracy the annual salary of each individual, Y, is determined by the formula
Y = 10,000 + 500S + 200T
where S is the number of years of schooling of the individual and T is the length of time, in years, of employment. X is the individual's age. Calculate Cov(X, Y), Cov(X, S), and Cov(X, T) for the sample of five individuals shown below and verify that
Cov(X, Y) = 500Cov(X, S) + 200Cov(X, T).
Explain analytically why this should be the case.
