Klein and Goldberger attempted to fit the following regression model tothe U.S. economy:Yi = ß1 + ß2X2i + ß3X3i + ß4X4i + uiwhere Y = consumption, X2 = wage income, X3 = nonwage, nonfarmincome, and X4 = farm income. But since X2, X3, and X4 are expected tobe highly collinear, they obtained estimates of ß3 and ß4 from crosssectionalanalysis as follows: ß3 = 0.75ß2 and ß4 = 0.625ß2. Using theseestimates, they reformulated their consumption function as follows:Yi = ß1 + ß2(X2i + 0.75X3i + 0.625X4i ) + ui = ß1 + ß2 Zi + uiwhere Zi = X2i + 0.75X3i + 0.625X4i .
a. Fit the modified model to the data in Table 10.11 and obtain estimatesof ß1 to ß4 .
b. How would you interpret the variable Z?