To explore more effective math teaching methods, a large high school conducted an experiment. In 2018 they randomly divided the 1200 grade 10 students into two groups. The control group (exp = 0, consisting of 600 students) followed the regular math program, and the experimental group (exp = 1, consisting of 600 students) followed an enhanced program featured by six-hour problem solving tutorial sessions per week on top of regular math classes. At the end of grade 10 (immediately after the experiment) and the end of grade 12 (two years after the experiment), all students took two math exams which were written and marked by selected math teachers from other schools. Suppose you are hired as an econometrician to evaluate the effectiveness of this experimental program. You have the grades from the above two math exams. In addition, you also have student's prior GPA (GPA at the end of grade 9). The students and their family characteristics were collected, such as gender, race, family income, education of the parents. Available school district variables include student to teacher ratio, poverty rate, median housing price, and percentage of household heads having a professional job. To evaluate the experiment, propose appropriate linear regression models. Make sure you clearly justify using or not using the variables given above and your model specifications. If you propose multiple models, discuss pros and cons of each model. Unbiasedness and magnitude of standard error of the key parameter estimate should be your main concerns