EC1) Suppose I want to know something about the study habits of undergraduate college students. I collect a random sample of 200 students and find that they spend 12 hours per week studying, on average, with a standard deviation of 5 hours. I am curious how their social lives might be associated with their studying behavior, so I ask the students in my sample how many other students at their university they consider "close friends." The sample produces an average of 6 close friends with a standard deviation of 2. Please use this information to answer the following questions. The correlation between these two variables is -.40. 1. Assume that "Hours spent studying" is the Y variable and "Close friends" is the X variable. Calculate the regression coefficient (i.e., the slope) and wrap words around your results. What, exactly, does this regression coefficient tell you? 2. What would the value of the standardized regression coefficient be in this problem? How do you know? 3. Calculate the intercept and wrap words around your result. 4. If you know that somebody studied had 10 close friends, how many hours per week would you expect her to study? 5. What, exactly, is a residual (when talking about regression)? 6. Regression is essentially a matter of drawing a straight line through a set of data, and the line has a slope and an intercept. In regression, how is it decided where the line should be drawn? In other words, explain the concept of least squares to me. 7. Now suppose that I add a second predictor variable to the regression model: Hours per week spent working for money. And suppose that the correlation between the hours spent working and hours spent studying is -.50. The correlation between the two predictor variables (number of close friends and hours spent working for money) is -.30. a. What effect do you think the addition of this second predictor variable will have on the overall amount of variance explained (R2 ) in the dependent variable? Why? b. What effect do you think the addition of this second predictor variable will have on the strength of the regression coefficient for the first predictor variable, compared to when only the first predictor variable was in the regression model? Why