3. Using the example on slide 18 of Lecture 21, (1) Given we have observations on a lot of students, conceptually, how could the three parameters a, b, c be estimated? (2) Consider another situation: Instead of half hour, if Joe stays 1 hour at school every day, how would his score change? The counterfactual framework X the amount of time a student spends in an after-school remedial program, H the amount of homework a student does, Ya student's score on the exam. A student Joe: (Encouragement) X a=0.5 (Homework) H (Exam score) c=0.4 b=0.7 Observed: X=0.5, H=1, Y= 1.5 Q: What would Joe's score have been had he doubled his homework? Could be a drug dosage decision in medical setting. X = Ux H = a.X+U Y=bX+c H+Uy uu, = 0 for all i,je (X,H,Y)