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Date Created: 03/14/15
Moshe Buchinsky Economics 103 Department of Economics Introduction to Econometrics UCLA Fall 2014 MidTerm Examination November 13 2014 Instruct ions 0 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 o 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 0 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 scantmn sheet Any question with more than one answer marked will not be counted 0 When you are nished with the exam please turn in both the exam questions and the scantron sheet 0 Cheating of any form will result in a score of 0 zero for the exam in addition to the normal university disciplinary action 0 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 Name Last Name UCLA ID Signature Exam Version B Please start solving the examinations only when you are instructed to do so Please stOp immediately when instructed to do so Good Luck Part I each question is worth 4 points Consider the following regression model M 51 525 6i for 73 1 N Let Eixi N 0 012 That is conditional on 561 61 has a distribution with a mean of 0 and a variance of 012 Let s22i 3m E2 wherefziix andyziiy 1 a Ni l l 7 Ni l z Ni l 1 Let also bland 2 be the ordinary least squares OLS estimates for 31 and 32 reSpectively 1 Let E y b1 92 then E 0 always b E need not be equal to zero c if y gt 0 then it must be that E gt 0 d if y gt 0 and E gt 0 then it must be that E gt 0 2 Assume that assumptions SR1 SR5 made in Chapter 2 hold then a E 92 32 only if in addition the distribution of 61 is normal I E 92 52 always c E 92 32 only if in addition 012 02 for all 73 ie 012 is a constant d E 92 7E 32 even if all the assumptions hold 3 Suppose one tested and rejected the null hypothesis H0 32 0 against H1 32 5 at the signi cant level 04 005 then one of the following must be true a He will reject H0 32 0 against H1 32 75 0 b He will reject H0 32 0 against H1 32 lt 1 c He will reject H0 32 0 against H1 32 lt 4 He will reject H0 32 0 against H1 32 gt 0 4 Suppose b2 2 75 86192 05 and N 42 The 90 con dence interval for 2 would be a 721761 10 602901 I 666 834 d 4241194 5 Suppose it is given that E 105 g 330 and b1 22 Then a 2 198 bb2 198 C 2 105 I 192 0105 6 Suppose that 0732 is that 100 1 oz con dence interval for 32 Assume that you want to test H0 32 0 against H1 32 75 0 with 04 being the type I error Under what condition will one reject H0 a There is not enough information provided to answer the question b If and only if 0 zero is in 0752 c The con dence interval 0732 provides no information that is useful for testing the above hypothesis I If and only if 0 zero is not in 0752 7 The larger is the variation in 561 73 1 n in the sample a The larger is the variance of 92 The smaller is the variance of 92 c The variation in 61 has no effect on the variance of 92 d The variation in 61 only affect the point estimate 92 8 Suppose that we ran a regression and we obtained 2 1 If we were to de ne a new variable 510 c 6 then a regression of y on 510 will yield an estimate for 32 say 93 that is equal to I I lc o c b 1c l o 9 Consider the hypotheses H0 32 0 against H1 32 gt 0 Using the statistic t 92379 92 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 effect on the likelihood of rejecting H0 I Sometimes answer a will be true and sometimes answer b will be true 10 11 12 13 14 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 The smaller is the SSE from a regression the larger is R2 Consider a 100 1 oz con dence interval for 31 given by 0731 Then a The larger is 04 the larger is the length of the interval The smaller is 04 the larger is the length of the interval c 04 does not have any effect on the length of the con dence interval d Whether or not 04 have an effect is determine by its magnitude Suppose that 92 15 36 92 105 and N 20 Then the 90 con dence interval for 32 IS a 20562356 5 125175 c 52 16711971 It is given that the 99 con dence interval for 32 is given by 63717 74817 where N 29 Then 92 the point estimate for 32 is a 2 125 I 52 0555 c 52 150 d 52 5123 Consider the null hypothesis H0 32 0 against the alternative hypothesis H1 32 lt 0 a If one were to reject H0 then one will accept H0 32 0 against H1 32 75 0 If one were to reject H0 then we cannot determine whether he she will also reject H0 32 0 against H1 32 75 0 c If one were to reject H0 then one will also reject H0 32 0 against H1 32 75 0 d If one were to accept H0 then one will also accept H0 32 0 against H1 32 75 0 15 16 17 Suppose one tested and rejected the null hypothesis H0 32 0 against H1 32 2 at the signi cant level 04 005 then one of the following must be true a He will reject H0 32 0 against H1 32 75 0 b He will reject H0 32 0 against H1 32 lt 0 I He will reject H0 32 0 against H1 32 gt 0 d He will reject H0 32 0 against H1 32 lt 2 The rejection region consists the values of test statistic that have I 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 The Gauss Markov Theorem establishes that the OLS estimator is a The best among all possible estimators for 32 The best among all linear unbiased estimators for 32 c The best among all linear unbiased estimators for 32 for which 61 has a normal distri bution d The best among all possible estimators that minimize the SSE Part II each question is worth 3 points Consider the following STATA output in which the summary statistics for four variables are provided y pizza 2 annual expenditure on pizza in dollars by an individual 62 income annual income in thousands of dollars of the individual 63 age age in years 64 female an indicator variable that take the value 1 if the person is a female and take the vale 0 zero otherwise There is also the output for three alternative regressions see the attached STATA output for this exam These regressions are 1 yz 51 525 6i 2 3 041 042562139 6i 3 3 51 325 33563139 m 4 3 71 725 73563139 745 M For each of the following questions determine Whether it is true false or it is not possible to determine Cannot be determined 1 On average a male s annual expenditure on pizza is about 184 more than that of a female I True b False c Cannot be determined 2 A 95 con dence interval for A 72 73 is given by 923 343 I True b False c Cannot be determined 3 In Model 4 one can reject the hypothesis that 73 0 at any reasonable 04 I True b False c Cannot be determined The variable 62 is economically more important than the variable 563 a True I False c Cannot be determined The estimated covariance between the estimates for 72 and 73 is negative I True b False c Cannot be determined In Model 2 the SSE is greater than the SSR I True b False c Cannot be determined Model 1 is meaningless a True I False c Cannot be determined One cannot have both age and income in the same regression a True False c Cannot be determined The results indicate that holding age income and gender constants a person spends on average 200 per year on pizza a True False c Cannot be determined 10 The R2 in Model 1 is an invalid measure of the goodness of t a True I False c Cannot be determined 11 From the output one cannot determine the 90 con dence interval for 33 in Model 3 a True I False c Cannot be determined 12 Comparing the results of Model 1 and Model 2 indicates that income is not an important determinant of eXpenditure on pizza for women a True I False c Cannot be determined
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