Suppose you are interested in estimating the effect of hours of work (hours) on total LSAT score (lsat). The population is all law school bound college seniors for a particular year. Here hours of work refers to any non-school related work that students might be involved in like work-study.

a. Suppose you are given a grant to run a controlled experiment. Explain how you would structure the experiment in order to estimate the causal effect of hours on lsat

b. Consider a more realistic case where students choose how much time to spend in non-school work and you can only randomly sample lsat and hours from the population. Write the population model as

i. lsat = f0 + f1 hours + u Where as usual in a model with an intercept, we can assume E(u)=0. List at least two factors contained in u (that is two variables that effect SAT score, but are not explicitly included in the model). Are these likely to have positive or negative correlation with hours?

c. In the equation from part (b), what should be the sign of f1 if the hours of work are significant?

d. In the equation from part (b), what is the interpretation of f0?