1. Table 1 presents a random sample of 8 observations on students' ACT (American College Test) and GPA (grade point average) scores. Consider the model GP Ai = Bo + B1ACT + Wi Student GPA ACT H 2.8 21 N 3.4 24 3.0 26 3.5 27 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 Table 1: Students's ACT and GPA scores a) Compute the OLS estimators B1 and Bo. b) Does Bo have a useful interpretation? c) What is the interpretation of B1? d) For each of the 8 observations, compute ui. Then, compute Ci-1 ui e) What is the predicted value of GPA when ACT = 20?2. Consider the following estimated regression equation that describes the relationship between a student's weight (measured in lb) and height (measured in feet): WEEHT = 100 + 6 HEIGHT a) First right down the linear regression equation from which we estimate the above results. b) What are the population regression fucntion in (a)? What are the population parameteres? c) What are 100 and 6 in the regression results? Are they unbiased? d) A student has height 5. What is the regression's prediction for that student's weight? e) In the sample, the sample average of HEIGHT is 4. What can you say about the sample average for WEIGHT? 3. This question tests your understanding of the concepts involved in regression analysis. Consider the model with one regressor, Y: = 160 +5195; +m- a) Write down the population regression function. Write down the sample regression function. 1)) What does Least Squares Assumption 1, E (u1| Xi) = 0, mean? In your answer, use the words \"other factors\". 0) Describe the other two \"Least Squares Assumptions\"? You only need to use one sentence for each assumption. (1) Is 51 a random variable? Is 31 an estimator? Is at: a random variable? Is {11- a random variable? (First: answer yes/ no. Then: short explanations if you are not sure about your yes/ no answers.)