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Worksheet: Regression Mechanics

(1)\ \ Pr(Passing\ Test)=\beta_{0}+\beta_{1}Homework\ Grade \\ (2) \ \ Pr(Passing\ Test)=\gamma_{0}+\gamma_{1}Study\ Time+\gamma_{2}Homework\ Grade

An RMDA professor can only estimate the first equation given the data she has at the end of the course. She is wondering if the relationship of homework grade on passing the test would be smaller or larger when one controls for study time. Unfortunately, she cannot observe study time. She assumes that study time is positively correlated with homework grade, however she is unsure if study time is positively or negatively correlated with passing the test. Give an answer to this professor under those two scenarios.

What is the marginal effect of being male?
What is the marginal effect of one more year of age?
The average men weights 150 pounds and 62 inches for tall. What is the marginal effect of one more year of age, at age 40?
The average men weights 150 pounds and 62 inches for tall. What is the predicted hourly wage for the average men who is a 40 years old?

wage=-11+-0.11weight+0.02weight^{2}+0.28height+3.49male

Let’s say we have this set up, where both female and black are binary variables, where the reference group is not-female and not black respectively:

Hourly\ Wage=\beta_{0}+\beta_{1}female+\beta_{2}black

What is the interpretation of $\beta_1$ ?
What is the interpretation of $\beta_0+\beta_1$ ?
What represents the average hourly wage for black females?
What represents the additional effect of being Black on hourly wages relative to not-black?

Hourly\ Wage=\beta_{0}+\beta_{1}female+\beta_{2}black+\beta_{3}female*black.

(1) \ \ Hourly\ Wage=\alpha_{0}+\alpha_{1}Education\ if\ female=1 \\ (2) \ \ Hourly\ Wage=\gamma_{0}+\gamma_{1}Education\ if\ female=0 \\ (3) \ \ Hourly\ Wage=\beta_{0}+\beta_{1}Female+\beta_{2}Education+\beta_{3}Female\times Education

What does $\alpha_0$ represent? What is the equivalence of $\alpha_0$ in equation (3)?
What does $\alpha_1$ represent? What is the equivalence of $\alpha_1$ in equation (3)?
What does $\gamma_0$ represent? What is the equivalence of $\gamma_0$ in equation (3)?
What does $\gamma_1$ represent? What is the equivalence of $\gamma_1$ in equation (3)?