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1. A researcher is studying the effect of parents' level of education on educational achievement of individuals. Using data on completed years of education (educ), mother's level of education (motheduc ), father's level of education (fatheduc), a measure of cognitive ability (abil), and logarithm of family income (1.income), the researcher estimates 4 models. Table (1) shows the OLS estimates for each model with standard errors in parentheses underneath each coefficient. The dependent variable in all the models is educ. , Model 1 Model 2 Model 3 Model 4 Independent variables I.income motheduc 0.27 (0.02) fatheduc 0.18 (0.03) 0.11 (0.02) 0.52 (0.03) 5 (0.2) 0.15 (0.03) 0.10 (0.02) 0.35 (0.03) 0.09 (0.01) 8.74 (0.31) abil 0.53 (0.03) 0.17 (0.03) 0.11 (0.02) 0.39 (0.03) 0.05 (0.01) 8.74 (0.31) 1230 3785.24 0.45 abil_squared Intercept 6.94 (0.32) 1230 3999.24 0.35 N SSR R-squared 1210 8.4 (0.12) 1230 3899.97 0.38 Table (1) 3541.2 0.49 a. Interpret the R-squared of the regression in model 1. [5 marks] b. Can you reject the claim that the returns to ability are linear? Be explicit about the hypothesis and any assumptions you make in order to answer the question. [6 marks] C. Carefully interpret the effect of increasing of l.income by 10. [6 marks] d. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. [5 marks]

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