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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 (l.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 L.income (0.2) 0.15 motheduc 0.27 0.18 0.17 (0.02) (0.03) 0.11 (0.02) 0.52 (0.03) 0.11 (0.02) 0.39 (0.03) 0.10 (0.02) 0.35 fatheduc abil 0.53 (0.03) (0.03) (0.03) 0.05 (0.03) 0.09 (0.01) 8.74 abil_squared ww (0.01) 8.74 6.94 (0.32) 1230 Intercept 8.4 (0.12) 1230 3899.97 0.38 Table (1) (0.31) 1230 (0.31) 1210 N SSR R-squared 3999.24 3785.24 3541.2 0.35 0.45 0.49 a. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. b. Why did the coefficient of motheduc decrease after adding variable fatheduc to the regression? Discuss and if necessary, incorporate the Gauss-Markov assumptions in your answer.

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 (l.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 L.income (0.2) 0.15 motheduc 0.27 0.18 0.17 (0.02) (0.03) 0.11 (0.02) 0.52 (0.03) 0.11 (0.02) 0.39 (0.03) 0.10 (0.02) 0.35 fatheduc abil 0.53 (0.03) (0.03) (0.03) 0.05 (0.03) 0.09 (0.01) 8.74 abil_squared ww (0.01) 8.74 6.94 (0.32) 1230 Intercept 8.4 (0.12) 1230 3899.97 0.38 Table (1) (0.31) 1230 (0.31) 1210 N SSR R-squared 3999.24 3785.24 3541.2 0.35 0.45 0.49 a. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. b. Why did the coefficient of motheduc decrease after adding variable fatheduc to the regression? Discuss and if necessary, incorporate the Gauss-Markov assumptions in your answer.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 (l.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 L.income (0.2) 0.15 motheduc 0.27 0.18 0.17 (0.02) (0.03) 0.11 (0.02) 0.52 (0.03) 0.11 (0.02) 0.39 (0.03) 0.10 (0.02) 0.35 fatheduc abil 0.53 (0.03) 0.09 (0.01) 8.74 (0.03) (0.03) (0.03) 0.05 abil_squared ww (0.01) 8.74 6.94 (0.32) 1230 Intercept 8.4 (0.12) 1230 3899.97 0.38 Table (1) (0.31) 1230 (0.31) 1210 N SSR R-squared 3999.24 3785.24 3541.2 0.35 0.45 0.49 a. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. b. Why did the coefficient of motheduc decrease after adding variable fatheduc to the regression? Discuss and if necessary, incorporate the Gauss-Markov assumptions in your answer.
Transcribed Image Text: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 (l.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 L.income (0.2) 0.15 motheduc 0.27 0.18 0.17 (0.02) (0.03) 0.11 (0.02) 0.52 (0.03) 0.11 (0.02) 0.39 (0.03) 0.10 (0.02) 0.35 fatheduc abil 0.53 (0.03) 0.09 (0.01) 8.74 (0.03) (0.03) (0.03) 0.05 abil_squared ww (0.01) 8.74 6.94 (0.32) 1230 Intercept 8.4 (0.12) 1230 3899.97 0.38 Table (1) (0.31) 1230 (0.31) 1210 N SSR R-squared 3999.24 3785.24 3541.2 0.35 0.45 0.49 a. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. b. Why did the coefficient of motheduc decrease after adding variable fatheduc to the regression? Discuss and if necessary, incorporate the Gauss-Markov assumptions in your answer.
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