Suppose we have data from a survey that asks students their GPA (GPA), the number of friends of the same sex they have (friends same), and the number of friends of the opposite sex they have (friends_opposite). We could use the data to estimate the impact of having friends of the opposite sex on a student's GPA. This research question is important because proponents of same-sex schools say that when kids have friends of the opposite sex, they become less focused on school and their GPAs suffer as a result. We'd like to test that theory. 1. Write down a model you could fit with this data that answers the research question. If you estimated your model, what would you expect could be reasonable values for the coefficients, and why? How would you interpret the coefficients? 2. Would you want to include friends_same^2 in your model? Why or why not? If you included that variable, what would be a reasonable value for its coefficient, and why? 3. We have to omit many variables that are important predictors of GPA from this model because of data limitations from the survey. Not including some of those variables would create omitted variable bias in the estimate we're most interested in (the effect of friends of the opposite sex on GPA), and some would not create omitted variable bias. Write down one variable that would be important in any model of GPA, but omitting it would not bias the estimate of the effect of friends of the opposite sex on GPA. Explain your answer. 4. Write down another variable that, since we have to omit it, would create omitted variable bias in the estimate of the effect of friends of the opposite sex on GPA. Explain your answer and also explain whether the bias would be positive or negative. 5. Explain the exogeneity assumption mathematically and intuitively as it relates to this model. Suppose we have data from a survey that asks students their GPA (GPA), the number of friends of the same sex they have (friends same), and the number of friends of the opposite sex they have (friends_opposite). We could use the data to estimate the impact of having friends of the opposite sex on a student's GPA. This research question is important because proponents of same-sex schools say that when kids have friends of the opposite sex, they become less focused on school and their GPAs suffer as a result. We'd like to test that theory. 1. Write down a model you could fit with this data that answers the research question. If you estimated your model, what would you expect could be reasonable values for the coefficients, and why? How would you interpret the coefficients? 2. Would you want to include friends_same^2 in your model? Why or why not? If you included that variable, what would be a reasonable value for its coefficient, and why? 3. We have to omit many variables that are important predictors of GPA from this model because of data limitations from the survey. Not including some of those variables would create omitted variable bias in the estimate we're most interested in (the effect of friends of the opposite sex on GPA), and some would not create omitted variable bias. Write down one variable that would be important in any model of GPA, but omitting it would not bias the estimate of the effect of friends of the opposite sex on GPA. Explain your answer. 4. Write down another variable that, since we have to omit it, would create omitted variable bias in the estimate of the effect of friends of the opposite sex on GPA. Explain your answer and also explain whether the bias would be positive or negative. 5. Explain the exogeneity assumption mathematically and intuitively as it relates to this model