econometric: the simple regression model

Could you do step by step?

2 In the simple linear regression model y - Bo + Bix + u, suppose that E(u) + 0. Letting co = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value. 3 The following table contains the ACT scores and the GPA (grade point average) for eight college stu- dents. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 2.8 21 3.4 24 3.0 26 3.5 27 CO V O UT A W N 3.6 29 3.0 25 2.7 25 3.7 30 (i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation GPA = Bo + B,ACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? (ii) Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero. (iii) What is the predicted value of GPA when ACT = 20? (iv) How much of the variation in GPA for these eight students is explained by ACT? Explain.6 Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and Mcclain (1995), the following equation relates housing price (price) to the distance from a recently built garbage incin- erator (dist): log(price) = 9.40 + 0.312 log(dist) n = 135, R2 = 0.162. Interpret the coefficient on log(dist). Is the sign of this estimate what you expect it to be? (ii) Do you think simple regression provides an unbiased estimator of the ceteris paribus elasticity of price with respect to dist? (Think about the city's decision on where to put the incinerator.) (iii) What other factors about a house affect its price? Might these be correlated with distance from the incinerator