3. Newspaper articles, Twitter posts, and politician interviews have all given statistics to back their claims. However, after taking 140A, you should be able to spot when these claims and statistics are extremely unreliable. The following is an excerpt from an article from cnbc.com titled "Here's how much more money you could make just from joining Joining a fraternity can cost you over $1,000 extra dollars a year in college, but odds are that you could end up secing a return on that investment. In a paper titled "Social Animal House: The Economic and Academic Consequences of Fraternity Membership." researchers from Union College found that going Greek raises your income by 36 percent down the line. The academic cost, meanwhile, is a small one: a 0.25 point drop in GPA on the traditional 4-point-scale. In other words, you might graduate with a 2.75 GPA while your classmate who didn't pledge ends up with a 3.00. But if he makes $75,000 a year, you could expect to make $102,000. These results suggest that fraternity membership causally produces large gains in social capital, which more than outweigh its negative effects on human capital." the researchers write. To those that are unfamiliar, a fraternity is an organization traditionally of men asso cinted together for various interests. These organizations typically require an extensive process to be accepted into the fraternity and membership is completely voluntary. The basic takeaway of the article is that if you join a fraternity in college, you will get more income . (a) Assuming that the researchers managed to randomly assign students at the one university to fraternities and find out their exact incomes later in life, write down the model (eg the regression formula) that would identify the causal effect of fraternity membership on income at the one university. You may assume you only need to index by i (egyou have a cross-section of data). Be sure to define what each of your variables are in bullet points. For example, one bullet point may read: Wage, is the wage of individual i at the university. (b) Upon reading the paper, you find that the researchers restricted their sample to only men under the age of 65 who are employed full-time. Briefly explain why this may discredit their interpretation that a fraternity membership increases income by 36 percent 3. Newspaper articles, Twitter posts, and politician interviews have all given statistics to back their claims. However, after taking 140A, you should be able to spot when these claims and statistics are extremely unreliable. The following is an excerpt from an article from cnbc.com titled "Here's how much more money you could make just from joining Joining a fraternity can cost you over $1,000 extra dollars a year in college, but odds are that you could end up secing a return on that investment. In a paper titled "Social Animal House: The Economic and Academic Consequences of Fraternity Membership." researchers from Union College found that going Greek raises your income by 36 percent down the line. The academic cost, meanwhile, is a small one: a 0.25 point drop in GPA on the traditional 4-point-scale. In other words, you might graduate with a 2.75 GPA while your classmate who didn't pledge ends up with a 3.00. But if he makes $75,000 a year, you could expect to make $102,000. These results suggest that fraternity membership causally produces large gains in social capital, which more than outweigh its negative effects on human capital." the researchers write. To those that are unfamiliar, a fraternity is an organization traditionally of men asso cinted together for various interests. These organizations typically require an extensive process to be accepted into the fraternity and membership is completely voluntary. The basic takeaway of the article is that if you join a fraternity in college, you will get more income . (a) Assuming that the researchers managed to randomly assign students at the one university to fraternities and find out their exact incomes later in life, write down the model (eg the regression formula) that would identify the causal effect of fraternity membership on income at the one university. You may assume you only need to index by i (egyou have a cross-section of data). Be sure to define what each of your variables are in bullet points. For example, one bullet point may read: Wage, is the wage of individual i at the university. (b) Upon reading the paper, you find that the researchers restricted their sample to only men under the age of 65 who are employed full-time. Briefly explain why this may discredit their interpretation that a fraternity membership increases income by 36 percent