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 (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 Lincome (0.2) 0.15 (0.03) 0.10 (0.02) 0.35 (0.03) 0.09 (0.01) 8.74 (0.31) 1210 3541.2 0.49 motheduc 0.27 0.18 (0.03) 0.11 (0.02) 0.52 (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 (0.02) fatheduc abil 0.53 (0.03) www abil_squared Intercept N SSR R-squared 6.94 (0.32) 1230 3999.24 0.35 8.4 (0.12) 1230 3899.97 0.38 Ti + 1) a. Interpret the R-squared of the regression in model 1. 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. c. Carefully interpret the effect of increasing of L.income by 10. d. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. e. 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.

Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables?    (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.     (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.       (d) Suppose a second regression model (Model 2) was generated using only…

If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?

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