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Part I: General Questions Answer all questions in this part. Question 1. You have estimated the following equation using OLS: yb = 33:75 + 1:45MALE where y is annual income in thousands and MALE is an indicator variable such that it is 1 for males and 0 for females. According to this model, the average income for females is? a. $33; 750 b. $35; 200 c. $32; 300 d. cannot be determined Question 2. Consider an economic model that uses income to predict monthly expenditures on transportation. The explanatory variable in this model is? a. income b. monthly expenditures on entertainment c. income elasticity d. demand for entertainment Question 3. Which of the following is NOT an assumption of the Simple Linear Regression Model a. The value of y, for each value of x, is y =1 +2x + e b. The variance of the random error e is V ar (e) = 2 c. The covariance between any pair of random errors ei and ej is zero d. The parameter estimate of 2 is unbiased. Question 4. In the OLS model, when the sample size (N) increases the variance of b2, Var(b2) a. increases b. decreases c. it does not change d. it cannot be determined give information provided 2 Question 5. How do you interpret the estimated value of 2 in the following equation: ln(ENT_EXP) = 1 + 2 (INCOME) + e where INCOME is annual household income (in thousands) and ENT_EXP is annual entertainment expenses? a. the income elasticity of entertainment b. when multiplied by 100 it is the percentage increase in entertainment expenses associated with an additional $1000 in income c. the increase in entertain expenses associated with a 1% increase in income d. the average of the logarithm of entertainment expenses for a household with zero income Question 6. You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coe¢ cient estimates): y = 97:25 +33:74x (3:86) (9:42) You want to test the following hypothesis: H0:2 = 12, against H1:2 6= 12. If you choose to reject the null hypothesis based on these results, what is the probability you have committed a Type I error? a. between .05 and .10 b. between .01 and .025 c. between .02 and .05 d. It is impossible to determine without knowing the true value of2 Question 7. Let c be a constant. For which alternative hypothesis do you reject H0 if t  t( ;N2)? a. H1: k = c b. H1:k 6= c c. H1:k > c d. H1:k < c Question 8. suppose the interval estimate for2 from the regression model y =1 +2x + e is given by [1:3; 2:2] then b2 the estimator for 2 must satisfy a. b2 < 1:3 b. b2 > 2:2 c. 1:3 < b2 < 2:5 d. cannot be determined based on the information provided Question 9. Consider the hypothesis H0: 2 = 0 against H1:2 6= 0. Suppose also that the 95% conÖdence interval for 2 is given by [I1; I2]. Then H0 is rejected if and only if a. zero belongs to the interval [I1; I2] b. zero does not belong to the interval [I1; I2] c. cannot be determined based on the information provided d. there is no connection between the hypothesis testing and interval estimate Question 10. Which of the following leads to a larger forecast errors? a. larger sample size, N b. variation in the explanatory variable, x, is large c. overall uncertainty in the model, as measured by 2 , is smaller d. the value of (x0 x) 2 is larger Question11. You have estimated a two variable model and your printout includes the following information sxy = 3614:00 sx = 12:72 sy = 394:61 SST = 758912:00 The is R2 for this regression model is: a. .72 b. .11 c. .03 d. .53 Question 12. Which of the following will change if you scale the dependent variable in a simple regression model? a. the p-value of2 b. the t-value of2 c. R2 d.1 Question 13. In the multiple regression model which of the following does NOT lead to larger variances of the least squares estimators b2 and V ar(b2)? a. larger error variances,  2 b. larger correlation between x2 and x3 c. smaller values of P i (xi2 x2) d. larger correlation between x 2 and y Question 14. Consider the multiple regression model given by yi = 1 +2xi2 +    +KxiK + ei For one to obtain unbiased estimates for1 ; :::;K, it must be that a. xi2; :::; xiK are uncorrelated b. E e 2 i  =  2 for all i1; :::; N c. E (ei) = 0 d.16= 0 Question 15. Consider the following regression model given by yi =1:1 +2xi2 + :5xi3 + ei with the variance-covariance matrix 0 @ :5 :2 :3 :2 :2 :1 :3 :1 :3 1 A The standard error for b2 +2b3 is a. 1:10 b. 0:40 ** c. 0:30 d. 0:1 Question 16. Consider the following regression model given by yi = 1:1 + 2xi2 + :5xi3 + ei with the variance-covariance matrix 0 @ :5 :2 :3 :2 :2 :1 :3 :1 :3 1 A Suppose N is very large, then the 95% conÖdence interval for 3 is a. [0:088; 1:088] ** b. [0:0; 1:0] c. [0:288; 1:288] d. [0:588; 1:588] Question 17. The critical value for a given p-value in the F-distribution depends on the degrees of freedom in the numerator and denominator. How do you Önd the degrees of freedom in the denominator? a. It is the number of observations minus the number of coe¢ cients estimated (N K) ***** b. It is the number of hypotheses being tested simultaneously (J) c. It is the number of coe¢ cients being estimated (K) d. It is the number of observations minus the number of hypotheses tested (N J) Question 18. How does omitting a relevant variable from a regression model a§ect the estimated coe¢ cient of other variables in the model? a. they are biased downward and have smaller standard errors 1. they are biased upward and have larger standard errors 2. they are biased and the bias can be negative or positive **** 3. they are unbiased but have larger standard errors Question 19. When collinear variables are included in an econometric model coe¢ cient estimates are a. biased downward and have smaller standard errors b. biased upward and have larger standard errors c. biased and the bias can be negative or posi d. unbiased but have larger standard errors Question 20. Running auxiliary regressions where each explanatory variable is estimated as a function of the remaining explanatory variables can help detect a. omitted relevant variables b. irrelevant variables included c. collinearity d. heteroskedasticity Question 21. A large company is accused of gender discrimination in wages. The following model has been estimated from the companyís human resource information ln (W AGE) = 1:439 + :0834 EDU + :0512 EXP ER + :1932MALE whereWAGE is hourly wage, EDU is years of education, EXP ER is years of relevant experience, andMALE indicates the employee is male. How much more do men at the Örm earn, on average? a. $1.21 per hour more than females b. 19.32% more than females **** c. $19.32 per hour d. $19,320 more per year than females Question 22. The following economic model predicts whether a voter will vote for an incumbent school board member INCUMBENT =1 + 2MALE + 3PART +4MARRIED+ 5KIDS where INCUMBENT =1 if the voter votes for them, 0 otherwise. MALE =1 if the voter is a male. P ART Y indicates the voter is registered with the same political party as the incumbent. MARRIED =1 for married voters, 0 otherwise. KIDS is the number of school age kids living in the voterís house. If you believe marriage a§ects male and female voters di§erently, which variable should you add to the economic model to allow you to test the hypothesis? a. MALE P ART Y b. MALE MARRIED *** c. MARRIED KIDS d. MARRIED P ART Y 7 Question 23. The adjusted R2 , i.e., R 2 , is a better measure than R2 because a. it adjust R2 for the number of variables in the regression b. it applies to cases where the regression does not have constant while R2 does not c. it provide a better measure for the sample variance of the dependent variable d. it applies for multiple regression with many variables. Question 24. The following model has been estimated ln(W AGE) =1 +2MALE +3MARRIED +4MALE MARRIED where MALE =1 if the individual is a male, MARRIED =1 for married individuals. On average, what is the wage di§erence between a married male and a married female? a.2 +4 b.2 c.4 d.2 +3 Question 25. Consider the Simple Linear Regression Model yi =1 +2xi + ei , with i = 1; : : : ; N. Let (b1; b2) be the OLS estimator and ( ~b1; ~b2) be another estimator. DeÖne the corresponding residuals e^i = yi b1 b2xi and e~i = yi ~b1 ~b2xi , then PN i=1 e^ 2 i  PN i=1 e~ 2 i a. always.*** b. only if ( ~b1; ~b2) is another ìlinearî estimator. c. only if Var(ei) =  2 for all i = 1; : : : ; N. d. only if E(ei) = 0 for all i = 1; : : : ; N. Question 26. Consider the Log-Log Regression ln(y) =1 +2 ln(x2) +3 ln(x3) + 4 ln(x2 x3) + e, where corr(x2; x3) = 0. Then, a. there is no problem in estimating such model at all. b. such model can be estimated but standard errors might be high. c. such model can be estimated but standard errors might be extremely low. d. such model cannot be estimated by OLS.*** Question 27. In the model y =1+ 2x2+ 3x3+e, with 3 > 0, you want to test H0:2= 3 =1 against HA :2= 3 6=1. Then a. you can use a t-test (or F-test) considering the null H0:23 =0.*** b. nonlinear approximation methods are required, otherwise the test cannot be implemented. c. you can use an F-test considering the joint null H0: 2 = 3 =1. d. you can use a t-test considering the simple null H0: 2 = 1. Question 28. Consider the model y =1 +2x + e with sample size N = 9900. The 95% conÖdence interval for b2 (the OLS estimate of2 ) is [2:38; 9:38]. The value of b2 is a. 3:50.*** b. 3:00. c. 3:00. d. there is no enough information to obtain such value. Question 29. In the model y =1+2x + e, the Gauss-Markov Theorem does NOT depend on the following assumption: a. The expected value of the error term e is zero, i.e., E(e) = 0. b. The variable x is not random and must take at least two di§erent values. c. The values e are normally distributed.*** d. All of the above. Question 30. For any given linear model, let b1 be the OLS estimator of1 . a. b1 is a random variable, whereas1 not.*** b. 1 is a random variable, whereas b1 not. c.Both b1 and 1 are random variables. d. b1 is not a random variable.1 either. Question 31. In certain country, most people are poor but some people is very, very, very rich. Let X be the wealth of an individual randomly chosen from the population of that country. Then, a. The mean of X is less than the median of X. In addition, the skewness of X is positive. b. The mean of X is less than the median of X. In addition, the skewness of X is negative. c. The mean of X is greater than the median of X. In addition, the skewness of X is positive.*** d. The mean of X is greater than the median of X. In addition, the skewness of X is negative. Question 32. If a variable is distributed normally, the Jarque-Bera statistic for a sample of that variable would be: a. negative and far from zero. b. negative and close to zero. c. positive and far from zero. d. positive and close to zero.*** Question 33. Your are considering running the following regression: wagei = 1 + 2 educi + 3malei + 4femalei + ui where: wagei is the wage per hour of individual i educi is the number of years of education, malei is a dummy variable that takes value 1 if individual is male femalei is a dummy variable that takes value 1 if individual is female. What can be said about the impact of being a man in the wages earned? a. The impact of being a man can be analyzed watching 3 . b. The impact of being a man can be analyzed watching 3 + 1 c. The impact of being a man can be analyzed watching 3 + 1 2 . d. This regression cannot be estimated due to perfect colinearity.*** Question 34. You are interested in estimating the impact of more police in the streets in the number of crimes committed in that area. You consider running the following regression: crimepercapitai = 1 + 2policei + 3unemploymenti + 4probconvictioni + ui where: crimepercapitai is the index of criminality in county i. policei is the number of police per capita in the county. probconvictioni is the probability of being convicted if you commit a crime in the county. unemploymenti is the unemployment rate in that county. What can you say about the impact of increasing the number per capita in county i? a. This impact can be measured by 2 . b. This impact can be measured by 1 + 2 c. In order to measure this impact we need to use an instrumental variable.*** d. This regression cannot be estimated due to perfect colinearity. 1 Question 35. You are interested in estimate the impact of one more year of education in the wages. You have decided to run the following regression: wagei = 1 + 2 educi + 3 blacki + 4 black educi + 5 experi + 6 exper2 i + ui where: wagei is the wage per hour of individual i educi is the number of years of education, blacki is a dummy variable that takes value 1 if individual declares himself to be black. blackeduci is the produc of the variable blacki and educi , i.e., blackeduci = black educi experi is the number of years of experience of individual i. You are interested in understanding the impact of one more year of education in individuals who declare themselves to be black. How can you measure this impact? a. This e§ect is given by 4 . b. This e§ect is given by 2 + 4 .*** c. This e§ect is given by 3 + 4 . d. This regression cannot be estimated due to perfect colinearity. Question 36. You want to run the following regression controlling for the county of origin of the individual. In your data set individuals come from k di§erent counties. wagei = 1 + 2 educi + 3agei + k j=2 j countyji + ui where: wagei is the wage per hour of individual i educi is the number of years of education, agei is the age of individual i, countyji is a series of dummies that take value one if individual i came from county j and zero for all other k 1 counties. You are interested in the interpretation of 4 . a. 4 indicates on average how much individuals from county 4 will make. b. 4 indicates on average how much individuals from county 4 will make more than the average of the sample. c. 4 indicates on average how much individuals from county 4 will make more than the average of individuals from county 1.*** d. This regression cannot be estimated due to perfect colinearity. 1 Part II: Multiple regression analysis on housing data Consider the regression out given below in Boca Raton Output. Answer all of the following questions: Question II.1. The results indicate that a traditional house would cost approximately a. $36; 000 less than a non-traditional house b. $27; 000 less than a non-traditional house c. $4; 700 less than a non-traditional house d. $18; 000 less than a non-traditional house Question II.2. The correlation between the coe¢ cients on the number of bedroom and the number of bath is a. 0:1005 b. 0:1835 *** c. 0:1835 d. 0:9001 Question II.3. The results indicate that if one test the hypothesis H0: 2 =    K = 0 against H1: At least one k 6= 0, k = 2; :::; K, one a. will accept the null hypothesis for = 0:01 b. will reject the null hypothesis for = 0:01 c. will reject the null hypothesis only for > 0:05 d. will accept the null hypothesis for > 0:05 Question II.4. Holding all variables constant, the result indicate that, on average, having a pool a. reduces the house price b. increase the house price c. does not have an e§ect on the house price ** d. the is not enough information to evaluate the e§ect of having a pool Question II.5. The 95% conÖdence interval for the coe¢ cient on SQFT is, approximately a. [74:46; 89:20] b. [148:92; 179:40] c. [74:46; 89:20] d. Cannot be determined Question II.6. the houses have waterfront b. 7:2% of the houses have waterfront *********** c. 27% of the houses have waterfront d. 2:7% of the houses have waterfront Question II.7. The results indicate that the e§ect of having a traditional house with a pool is a. positive b. has no e§ect c. cannot be determined d. negative ** 13 Part III: Wage Regression Consider the regression out given below in Wage Regression Analysis Output Answer all of the following questions: Question III.1. The variable NorthEast is dropped because of a. Irrelevant variables included b. Heteroskedasticity c. Collinearity d. Omitted relevant variables Question III.2. Individuals in MidWest earn on average 4.232 less than a. individuals in South b. individuals in West c. individuals in NorthEast d. individuals other than MidWest Question III.3. The results indicate that if one test the null hypothesis H0 : 3 = 5 = 6 = 0 against H1: At least one k 6= 0; k = 3; 5; 6, one 1. one will accept the null hypothesis for = 0:05 b. one will reject the null hypothesis for = 0:05 c. one will reject the null hypothesis for = 0:1 d. have no information from the output Question III.4. Consider a restricted model with the form W AGE = 1 + 2EDU 1. Which of the following statement is true? a. The restricted model will have a smaller R2 compared to the original model b. The restricted model will have a bigger R2 compared to the original model c. The R2 of the restricted model will be bigger if number of observations is large enough d. None of the above 14 Part IV: Corn Production Consider the regression out given below in Corn Production Output Answer all of the following questions: Question IV.1 The coe¢ cient 2 has the following interpretation: a. A unit increase in capital leads to a 265% increase in the production of corn.*** b. A unit increase in capital leads to a 26.5% increase in the production of corn. c. A unit increase in capital leads to a 2.65% increase in the production of corn. d. A unit increase in capital increases production of corn by 2.65 kilos. Question IV.2. According to above result, we reject the null H0 : 3 4 = 0 against HA : 3 4 6= 0: a. At 1%. b. At 5%. c. At 1% and 5%*** d. There is no enough information. Question IV.3. According to above result, we reject the null H0 : 4 = 5 = 0 against HA : 4 6= 0 or 5 6= 0: a. At 1%. b. At 5%. c. At 1% and 5% d. There is no enough information *** Question IV.4. Considering above output results, the consequence of heteroskedasticity in e is: a. Invalid conÖdent intervals. b. Invalid p-values. c. All of the above.*** d. Biased estimates of the coe¢ cients. Part V: Wage Regression for Rich and Poor Output Consider the regression out given below in Wage Regression for Rich and Poor Output Answer all of the following questions: Question V.1. If we were to take im_rich out of the regressors, but include native, the estimated coe¢ cient of im_poor would now be: a. between -0.30 and -0.15***. b. between -0.15 and 0. c. between 0 and 0.15. d. between 0.15 and 0.30. Question V.2. If we were to take im_rich out of the regressors, but include native, the R2 would now be: a. higher than in the original model. b. equal to the one of the original model***. c. lower than in the original model. d. there is not enough information. Question V.3. Consider the original model. Suppose that we think that the wage has a higher variability among immigrants than among natives. Then, a. The OLS estimator would still be unbiased. The estimated conÖdence intervals would still be valid. b. The OLS estimator would still be unbiased. The estimated conÖdence intervals would not be valid.*** c. The OLS estimator would be biased. The estimated conÖdence intervals would still be valid. d. The OLS estimator would be biased. The estimated conÖdence intervals would not be valid. Question V.4. Consider the original model. We think that education has a positive e§ect in wages, but immigrants from poor countries are on average less educated than natives. We conclude that: a. The OLS estimator of im_poor has a positive bias. We expect 2 to be greater than - .1009196. b. The OLS estimator of im_poor has a positive bias. We expect 2 to be less than -.1009196. c. The OLS estimator of im_poor has a negative bias. We expect 2 to be greater than -.1009196.*** 16 d. The OLS estimator of im_poor has a negative bias. We expect 2 to be less than -.1009196. Question V.5. If we had measured the wages in cents instead of dollars: a. The constant of the model would be larger, the coe¢ cient of im_rich would be larger. b. The constant of the model would be larger, the coe¢ cient of im_rich would be the same***. c. The constant of the model would be the same, the coe¢ cient of im_rich would be larger. d. The constant of the model would be the same, the coe¢ cient of im_rich would be the same. 17 Boca Raton ñOutput 18 Wage Regression Analysis Output The following economic model predicts individualís wage based on education and region. E (W AGE) = 1 + 2EDU + 3M idW est + 4NorthEast + 5South + 6W est where M idW est = 1 if Region == ìmidwest,îNorthEast = 1 if Region == ìnortheast,îSouth = 1 if Region == ìsouth,îW est = 1 if Region == ìwestî STATA Command: table region ---------------------- region | Freq. ----------+----------- midwest | 337 northeast | 57 south | 248 west | 178 ---------------------- STATA Command: reg wage edu NorthEast MidWest South West Source | SS df MS Number of obs = 820 -------------+------------------------------ F( 4, 815) = 16.07 Model | 13416.8521 4 3354.21302 Prob > F = 0.0000 Residual | 170118.196 815 208.733983 R-squared = 0.0731 -------------+------------------------------ Adj R-squared = 0.0686 Total | 183535.048 819 224.096518 Root MSE = 14.448 ------------------------------------------------------------------------------ wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- edu | 1.206153 .16092 7.50 0.000 .8902869 1.52202 NorthEast | (dropped) MidWest | -4.232238 2.069481 -2.05 0.041 -8.294378 -.1700976 South | -4.99543 2.122288 -2.35 0.019 -9.161225 -.8296364 West | -5.825008 2.198793 -2.65 0.008 -10.14097 -1.509043 _cons | 2.472763 2.818565 0.88 0.381 -3.05974 8.005266 ------------------------------------------------------------------------------ STATA Command: test (_b[MidWest]=0)(_b[South]=0)(_b[West]=0) ( 1) MidWest = 0 ( 2) South = 0 ( 3) West = 0 F( 3, 815) = 2.48 Prob > F = 0.0601 19 Corn Production Output Consider the following model ln(corn) = 1 + 2 capital + 3 labor + 4 land + 5 (labor land) + e; where corn denotes the production of corn (in pounds), while the regressors have the obvious meaning. Based on the next STATA output, answer the questions below. (lab_lan stands for labor land as usual). STATA Command: reg ln_corn capital labor land lab_lan Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 4, 995) =26509.48 Model | 145016.524 4 36254.1309 Prob > F = 0.0000 Residual | 1360.75347 995 1.36759142 R-squared = 0.9907 -------------+------------------------------ Adj R-squared = 0.9907 Total | 146377.277 999 146.523801 Root MSE = 1.1694 ------------------------------------------------------------------------------ ln_corn | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- capital | 2.654115 .0098252 270.13 0.000 2.634835 2.673396 labor | -.0045532 .3219485 -0.01 0.989 -.6363292 .6272228 land | .4869289 .21929 2.22 0.027 .056605 .9172528 lab_lan | .4458096 .0547902 8.14 0.000 .338292 .5533272 _cons | 2.946969 1.284514 2.29 .426302 5.467636 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ STATA Command: test land = labor . test land = labor ( 1) - labor + land = 0 F( 1, 995) = 8.08 Prob > F = 0.0046 20 Wage Regression for Rich and Poor Output Consider the following model ln(wage) = 1 + 2 im_poor + 3 im_rich + e; where wage denotes the hourly wage in dollars, emphim_poor takes the value of 1 if the person is an immigrant from a poor country (0 otherwise), im_rich takes the value of 1 if the person is an immigrant from a rich country (0 otherwise). Consider also the variable native deÖned as native = 1 im_poor im_rich; . After estimating the aforementioned model in Stata, the following result is obtained: . reg ln_wage im_poor im_rich Source | SS df MS Number of obs = 6770 -------------+------------------------------ F( 2, 6767) = 28.88 Model | 31.2933892 2 15.6466946 Prob > F = 0.0000 Residual | 3666.08138 6767 .541758738 R-squared = 0.0085 -------------+------------------------------ Adj R-squared = 0.0082 Total | 3697.37477 6769 .546221712 Root MSE = .73604 ------------------------------------------------------------------------------ ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- im_poor | -.1009196 .0210986 -4.78 0.000 -.1422795 -.0595597 im_rich | .1188251 .0260645 4.56 0.000 .0677303 .1699198 _cons | 2.719635 .0115901 234.65 0.000 2.696915 2.742356 ------------------------------------------------------------------------------

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1) A) If the indicator variables MALE is contingent on the employees gender, then for a female the average income y=33.75.
2) A) An economic model that uses income to predict monthly expenditures on transportation is clearly dependent on income.
3) D) The rest of these answers are not assumptions of the simple linear regression model.
4) A) If the sample size increases the variance of b2 then clearly Var(b2) increases.
5) B) This coefficient is the percentage increase. ...
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