Suppose an economist specifies a "human capital" model in which earnings or income is the dependent variable, and years of education and IQ are the independent variables. Income is represented by Y, IQ by X1, and years of education by X2. The underlying theory behind the model is that IQ and education should both have an impact on the earnings of individuals. The data (hypothetical) available to test this theory are presented in this table.
Income-IQ-Education Table
Income (Y) IQ (X1) Education (X2)
$5000 80 9
6000 95 8
7000 100 10
8000 101 10
9000 103 11
10000 115 14
11000 105 15
12000 116 13
13000 120 16
14000 110 17
a) Estimate the regression equation
b) Conduct the significance of the regression test (alpha = 5%)
c) Calculate R^2
d) Test if the IQ variable is a significant determinant of changes in income (alpha = 1%). Do the same for education (alpha = 5%)
e) Find the point estimate of income when IQ = 120 and education = 16.