Use the data in the Exercise 9.39 to calculate the annual change in income and consumption, for example, in 1961 Y − Y₋₁ = 11.05 − 10.86 = 0.19.

a. Draw a scatter diagram using these annual changes.

b. Estimate the consumption function (C −C₋₁) = α+β(Y −Y₋₁)+ε.

c. Calculate the residuals e = (C −C₋₁) = [a+b(Y −Y₋₁)] for each year and make a scatter diagram with e on the vertical axis and the year on the horizontal axis.

d. Do you see anything in this residuals plot that suggests that the least squares assumptions might be violated?