Anumber of organizations and governments are considering policies to supply students with access to free computers, in an effort to boost learning outcomes. suppose that you want to learn about the effect of having a free computer on test scores. for a sample of high school students, you collect data on test scores (test), parent's income (inc), and whether they have a computer at home (comp) suppose that a local organization held a lottery, and offered computers at random to a number of students, indicated by freecomp. suppose that among the population who were not offered a free computer, 60% have a computer, whereas after the lottery, 90% of people offered a computer had a computer. compare the specifications a. test - po +b1comp+ u and test-bo + bıfreecomp + u both tell you something different about the effect of computers on test scores. describe the limitations of each approach b. you are concerned that household income may be correlated with test scores for a variety of reasons. suggest an alternate specification that holds income constant, and discuss how you anticipate it changing inference using each estimated b1 above propose a "treatment on the treated" estimator for the free computer lottery c. d. you think computers might have two different effects on test scores. on the one hand, they are a productive tool which can learning. on the other hand, they open up recreational opportunities (like social networking) which may not be very useful for learning. as a result, you wonder what the effects of a free computer would be if you could hold recreational screentime constant. that is, you would like to estimate test-ße + β1freecomp + β2screentime+ u however, in practice you cannot observe screentime. you have two options: either you can just use whether they have a smart phone as a proxy variable for screentime (variable smartphone), or you can ask the students to report how much screentime they spend per day (rep screentime) describe algebraically how each approach will affect estimation of b1 and b2 in the equation for part d, and the analogue to mlr4 which is necessary to grant unbiased estimates. discuss