UCLA ECON 103 2014 fall midterm

Economics 103Department of Economics Introduction to EconometricsUCLA Fall, 2014Mid-Term ExaminationInstructions: This is a 1 hour and 15 minutes open-book in-class exam. You are allowed to use your text book, your notebook and a calculator. No connection to the internet via WiFi or any other method is allowed. It is not permitted to use any kind of phone. The only devices that are allowed are iPad (or equivalent) and a laptop, and ONLY for the purpose of accessing you e-book version of the course textbook. Please answer all the questions. Please choose the best answer among all available answers. Only one answer is the best answer! Please mark one, and only one, answer on the scantron sheet. Any question with more than one answer marked will not be counted. When you are ?nished with the exam, please turn in both the exam questions and the scantron sheet. Cheating of any form will result in a score of 0 (zero) for the exam, in addition to the normal university disciplinary action. Please sign below that you have read, understood, and ful?lled all of the above instructions and conditions.Please ?ll in the following personal information:First NameLast NameUCLA ID #SignatureExam Version BPlease start solving the examinations only when you are instructed to do so.Please stop immediately when instructed to do so.Part I (each question is worth 4 points):Consider the following regression model:yi = 1 + 2xi + ei;for i = 1; :::;N. Let eijxi ????0; 2i. That is, conditional on xi, ei has a distribution with a meanof 0 and a variance of 2i. Lets2x =1NXNi=1(xi ???? x)2 ; where x =1NXNi=1xi; and y =1NXNi=1yi: (1)Let also b1and b2 be the ordinary least-squares (OLS) estimates for 1 and 2, respectively.1. Let e = y ???? b1 ???? b2x, then,(a) e = 0 always(b) e need not be equal to zero(c) if y > 0, then it must be that e > 0(d) if y > 0 and x > 0, then it must be that e > 02. Assume that assumptions SR1-SR5 made in Chapter 2 hold, then:(a) E (b2) = 2 only if in addition the distribution of ei is normal.(b) E (b2) = 2 always.(c) E (b2) = 2 only if in addition 2i= 2 for all i, i.e., 2iis a constant.(d) E (b2) 6= 2 even if all the assumptions hold.3. Suppose one tested and rejected the null hypothesis H0: 2 = 0 against H1: 2 = 5 at thesigni?cant level = 0:05, then one of the following must be true:(a) He will reject H0: 2 = 0 against H1: 2 6= 0.(b) He will reject H0: 2 = 0 against H1: 2 < ????1.(c) He will reject H0: 2 = 0 against H1: 2 < 4.(d) He will reject H0: 2 = 0 against H1: 2 > 0.4. Suppose b2 = :75, se (b2) = :05, and N = 42. The 90% con?dence interval for b2 would be:(a) [:721; :761].(b) [:602; :901].(c) [:666; :834].(d) [:424; 1:194].25. Suppose it is given that x = 10:5, y = 3:30, and b1 = 2:2. Then(a) b2 = 19:8(b) b2 = ????19:8(c) b2 = 10:5(d) b2 = 0:1056. Suppose that CI2 is that 100 (1 ???? )% con?dence interval for 2. Assume that you wantto test H0: 2 = 0 against H1: 2 6= 0 with being the type I error. Under what conditionwill one reject H0?(a) There is not enough information provided to answer the question.(b) If and only if 0 (zero) is in CI2 .(c) The con?dence interval CI2 provides no information that is useful for testing the abovehypothesis.(d) If and only if 0 (zero) is not in CI2 .7. The larger is the variation in xi, i = 1; :::n, in the sample:(a) The larger is the variance of b2.(b) The smaller is the variance of b2.(c) The variation in xi has no e¤ect on the variance of b2.(d) The variation in xi only a¤ect the point estimate b2.8. Suppose that we ran a regression and we obtained b2 = 1. If we were to de?ne a new variablex = c x, then a regression of y on x will yield an estimate for 2, say b2, that is equal to(a) b2= 1=c.(b) b2= c.(c) b2= 1 + c.(d) b2= 1 ???? c.9. Consider the hypotheses H0: 2 = 0 against H1: 2 > 0. Using the statistic t = b2= b se (b2)for testing H0 against H1:(a) The smaller the sample size, the more likely it is that we reject H0.(b) The larger the sample size, the more likely it is that we reject H0.(c) The sample size has no e¤ect on the likelihood of rejecting H0.(d) Sometimes answer (a) will be true and sometimes answer (b) will be true.310. Consider the SSE from a given regression. Which of the following statements is correct?(a) There is no direct link between SSE and R2.(b) To determine how high R2 is we need to know both SSR and SSE.(c) The larger is the SSE from a regression the larger is R2.(d) The smaller is the SSE from a regression the larger is R2.11. Consider a 100 (1 ???? )% con?dence interval for 1 given by CI1 . Then,(a) The larger is the larger is the length of the interval.(b) The smaller is the larger is the length of the interval.(c) does not have any e¤ect on the length of the con?dence interval.(d) Whether or not have an e¤ect is determine by its magnitude.12. Suppose that b2 = 1:5, se (b2) = 10:5, and N = 20. Then the 90% con?dence interval for 2is:(a) [????20:56; 23:56].(b) [1:25; 1:75].(c) [????:5; 2].(d) [????16:71; 19:71].13. It is given that the 99% con?dence interval for 2 is given by [????6:3717; 7:4817], where N = 29.Then b2, the point estimate for 2, is(a) b2 = 1:25(b) b2 = 0:555(c) b2 = 1:50(d) b2 = 5:12314. Consider the null hypothesis H0: 2 = 0 against the alternative hypothesis H1: 2 < 0.(a) If one were to reject H0 then one will accept H0: 2 = 0 against H1: 2 6= 0.(b) If one were to reject H0 then we cannot determine whether he/she will also reject H0:2 = 0 against H1: 2 6= 0.(c) If one were to reject H0 then one will also reject H0: 2 = 0 against H1: 2 6= 0.(d) If one were to accept H0 then one will also accept H0: 2 = 0 against H1: 2 6= 0.415. Suppose one tested and rejected the null hypothesis H0: 2 = 0 against H1: 2 = 2 at thesigni?cant level = 0:05, then one of the following must be true:(a) He will reject H0: 2 = 0 against H1: 2 6= 0.(b) He will reject H0: 2 = 0 against H1: 2 < 0.(c) He will reject H0: 2 = 0 against H1: 2 > 0.(d) He will reject H0: 2 = 0 against H1: 2 < 2.16. The rejection region consists the values of test statistic that have:(a) Low probability of occurring when the null hypothesis is true.(b) High probability of occurring when the null hypothesis is true.(c) Low probability of occurring regardless of whether the null hypothesis is true or not.(d) High probability of occurring regardless of whether the null hypothesis is true or not.17. The Gauss-Markov Theorem establishes that the OLS estimator is:(a) The best among all possible estimators for 2.(b) The best among all linear unbiased estimators for 2.(c) The best among all linear unbiased estimators for 2 for which ei has a normal distri-bution.(d) The best among all possible estimators that minimize the SSE.5Part II (each question is worth 3 points):Consider the following STATA output in which the summary statistics for four variables areprovided:yi = pizza = annual expenditure on pizza in dollars by an individual.x2i = income = annual income in thousands of dollars of the individual.x3i = age = age in years.x4i = female = an indicator variable that take the value 1 if the person is a female, and take thevale 0 (zero) otherwise.There is also the output for three alternative regressions (see the attached STATA output forthis exam). These regressions are:1: yi = 1 + 2x4i + ei2: yi = 1 + 2x2i + ei3: yi = 1 + 2x2i + 3x3i + vi4: yi =1 +2x2i +3x3i +4x4i + uiFor each of the following questions determine whether it is true, false, or it is not possible todetermine (Cannot be determined):1. On average, a male?s annual expenditure on pizza is about $184 more than that of a female.(a) True(b) False(c) Cannot be determined2. A 95% con?dence interval for =2 +3 is given by [????9:23;????3:43].(a) True(b) False(c) Cannot be determined3. In Model 4, one can reject the hypothesis that3 = 0 at any reasonable .(a) True(b) False(c) Cannot be determined64. The variable x2i is economically more important than the variable x3i.(a) True(b) False(c) Cannot be determined5. The estimated covariance between the estimates for2 and3 is negative.(a) True(b) False(c) Cannot be determined6. In Model 2 the SSE is greater than the SSR.(a) True(b) False(c) Cannot be determined7. Model 1 is meaningless.(a) True(b) False(c) Cannot be determined8. One cannot have both age and income in the same regression.(a) True(b) False(c) Cannot be determined9. The results indicate that, holding age, income, and gender constants, a person spends, onaverage, $200 per year on pizza.(a) True(b) False(c) Cannot be determined710. The R2 in Model 1 is an invalid measure of the goodness-of-?t.(a) True(b) False(c) Cannot be determined11. From the output, one cannot determine the 90% con?dence interval for 3 in Model 3(a) True(b) False(c) Cannot be determined12. Comparing the results of Model 1 and Model 2 indicates that income is not an importantdeterminant of expenditure on pizza for women.(a) True(b) False(c) Cannot be determined