ECON 271/371, Trimester Assignment

Multiple ChoiceSelect the answer that is most appropriate and CIRCLE on the MULTIPLE CHOICEANSWER SHEET provided on page 10. Answers not shown on Multiple Choice AnswerSheet, will not be marked.ECON271 students: answer 10 parts (from 1 to 10), each part carries 3 marks.ECON371 students: answer 15 parts (from 1 to 15), each part carries 2 marks.1.Which of the following is NOT an assumption of the Simple Linear Regression Model?a)b)The variance of the random error e is var(e)= 2c)The covariance between any pair of random errors ei and ej is zerod)2.The value of y, for each value of x, is y = 1 + 2x + eThe parameter estimate of 1 is unbiased.In the OLS model, what happens to var(b1) as the sample size (N) increases?a)b)it decreasesc)it does not changed)3.it also increasescannot be determined without more informationFor which alternative hypothesis do you reject H0 if |t| t (/2,N-2)?a)b)k cc)k > cd)4.k = ck < cIn which case would testing the null hypothesis involve a two-tailed statistical test?a)H1: Incentive pay for teachers does affect student achievementb)H1: Higher sales tax rates does not reduce state tax revenuesc)H1: Extending the duration of unemployment benefits does not increase the length ofjoblessnessd)H1: Smoking does not reduce life expectancy5. The overall regression F-statistic tests the null hypothesis thata)all slope coefficients are zero.b)all slope coefficients and the intercept are zero.c)the intercept in the regression and at least one, but not all, of the slope coefficients iszero.d)the slope coefficient of the variable of interest is zero, but that the other slopecoefficients are not.6.When should a researcher consider transforming the explanatory variable in a simple linearregression model?a)b)to get a coefficient estimate with the sign predicted by economic theoryc)to reduce the variation in the explanatory variabled)7.when a data plot suggests there is a non-linear functional formto maximize SSRHeteroskedasticity is a violation of which assumption of the MR model?a)The values of each xi are not random and are not exact linear functions of the otherexplanatory variablesb)c)d)8.E(yi) = 1 + 2xi2 + 3xi3 + . + kxik, E(ei) = 0var(yi.) = var(ei) = 2cov(yi, yj) = cov(ei, ej) = 0;(ij)How do you interpret the estimated value of 2 in the following model?ln(y) = 1 + 2 * ln(x)a)the slope of the line representing the relationship between y and xb)the elasticity of y with respect to xc)cannot be determined without more informationd)the mean value of ln(y) when ln(x) = 0.9. In the multiple regression model, the t-statistic for testing that the slope is significantly differentfrom zero is calculateda)b)from the square root of the F-statistic.c)by multiplying the p-value by 1.96.d)10.by dividing the estimate by its standard error.using the adjusted R2 and the confidence interval.When autocorrelation is present, which assumption of the linear regression model is incorrect?a)E(et)=0b)var (et)=2c)cov(et, es) =0, tsd)et N(0,2)For 371 Students Only:11.The following Mincer equation has been used to estimate wages:ln (Y) = ln (Yo) + 2EDU + 3 EXPER + 4 EXPER2 + ewhere Y is wage, Y0 is wage of someone with no education or experience, EDU is years ofeducation and EXPER is experience in the field.If you suspect males earn higher wages than females and that the wage difference increases witheducation, how would you adjust the econometric model to estimate wages?a)b)include an interaction term equal to MALE* EXPERc)include an indicator variable for MALE and one for FEMALEd)12.include a binary variable for gender, MALEinclude a binary variable for MALE and an interaction term equal to MALE * EXPERHow should k in the general multiple regression model be interpreted?a)The number of units of change in the expected value of y for a 1 unit increase in xk whenall remaining variables are unchangedb)the magnitude by which xk varies in the modelc)the amount of variation in y explained by xk in the modeld)the number of variables used in the model.13.A model estimated using a dataset with 65 observations generates the following results.VariableStd. Errort-statisticP>|t|x2x3x4x5Constant-0.012640.5957921.1245890.3237428.860160.0055190.0144820.8771920.0607091.766116-2.2893741.139341.2820325.3326615.0167490.0220.0000.2000.0000.000If you want to test the hypothesis that 3 =0.45, what is the test statistic from this sample?a)b)10.067c)31.072d)14.41.1390.000Which of the following is not an assumption of the multiple regression model?a)The values of each xik are not random and are not exact linear functions of the otherexplanatory variables.b)c)The least squares estimators are BLUE.d)15.var(yi.) = var(ei) = 2cov(yi, yj) = cov(ei, ej) = 0;(ij)How are coefficient estimates from WLS (weighted least squares) interpreted?a)they must be scaled up by the weight used in order to calculate marginal effectsb)there is no difference in interpretation since each observation is scaled by the samedivisorc)take the inverse of the natural logarithm of the coefficient to find marginal effectsd)They should only be used for hypothesis testing. Coefficient estimates from the unweighted, original model should be used for prediction.Question 2 (30 marks)A professor investigated some of the factors that affect an individual student’s final grade in hiscourse. He proposed the multiple regression model y = 0 + 1×1 + 2×2 + 3×3 + e, where y is the finalmark (out of 100), x1 is the number of lectures skipped, x2 is 1 for male and is 0 otherwise, and x3 isthe mid-term test mark (out of 100). The professor recorded the data for 50 randomly selectedstudents. The computer output is shown below.Dependent Variable: YMethod: Least SquaresDate: 03/11/12 Time: 14:35Sample: 1 50Included observations: 49VariableCx1x2x3R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodDurbin-Watson statCoefficient41.6-4.18-1.170.630.300916Std. Errort-Statistic17.82.3371.66-2.5181.13-1.0350.134.846Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statisticProb(F-statistic)37168688Prob.6.5581.Write the estimated regression model and explain the meaning of slope coefficients.2.What is the Goodness- of- Fit? What does this statistic tell you?3.Do these data provide enough evidence to conclude at the 5% significance level that the modelis overall significant?4.Do these data provide enough evidence to conclude at the 5% significance level that the finalmark and the number of skipped lectures are related?5.Do these data provide enough evidence at the 5% significance level to conclude that the finalmark of male students are lower than of female students?6.Do these data provide enough evidence at the 1% significance level to conclude that the finalmark and the mid-term mark are positively related?Question 3 (20 marks)1.Consider a regression model:Model 3.1:Dependent Variable: YMethod: Least SquaresDate: 03/11/10 Time: 15:13Sample: 1975:1 1990:4Included observations: 64VariableCoefficientStd. Errort-StatisticProb.CX1X2X3X4X5X625531.6750.11645630.4908-44.38278-41.8123314.06459-150.67956606.08522.97292310.332714.0302173.7498747.5273039.304573.8648712.1815442.031661-3.163371-0.5669480.295927-3.8336370.00030.03330.04690.00250.57300.76840.0003R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodDurbin-Watson stat0.4935230.440210249.08943536594.-440.24541.955138Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statisticProb(F-statistic)2488.594332.922013.9764214.212559.2570190.000000Model 3.2:Breusch-Godfrey Serial Correlation LM Test:F-statisticObs*R-squared1.5093101.679655ProbabilityProbability0.2243830.194970Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 03/11/10 Time: 19:20Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.CX1X2X3X4X5X6RESID(-1)-623.1706-0.743301-49.84859-0.655310-8.068256-1.8749366.3646030.1640686596.30022.87897311.608513.9781373.7157047.3409839.471590.133547-0.094473-0.032488-0.159972-0.046881-0.109451-0.0396050.1612451.2285400.92510.97420.87350.96280.91320.96850.87250.2244R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodDurbin-Watson stata)0.026245-0.095475247.98393443778.-439.39441.914130Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statisticProb(F-statistic)-8.95E-12236.931313.9810714.250930.2156160.980351Carry out the Durbin-Watson test for first-order autocorrelation at the 5% significancelevel.b)2.Carry out the LM test for first-order autocorrelation at 10% significance level.(For 371 Students only):The model yt = 8 + 2.5xt + 0.35yt-1 is estimated using regression analysis applied to time-seriesdata. What is the effect of a 1-unit increase in x in period t and (t+1)?Question 4 (20 marks)EVIEWS outputs from several regressions are shown below. The variable definitions are_WAGE=Wage in dollarsEDUC=Education in yearsEXPER=Experience in yearsAGE=Age in yearsGENDER=1 if male 0 if femaleRACE=1 if black 0 otherwiseModel 4.1Dependent Variable: LWAGEMethod: Least SquaresDate: 03/11/10 Time: 14:35Sample: 1 49Included observations: 49VariableCoefficientStd. Errort-StatisticProb.CEDUCEXPERAGEGENDERRACE6.8643660.0529870.020776-0.0022500.2426100.0714790.1861270.0171070.0063210.0038040.0716450.08154336.880023.0974323.286999-0.5913823.3863000.8765750.00000.00340.00200.55740.00150.3856R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodDurbin-Watson stat0.4709160.4093950.2403442.4839043.5307331.708658Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statisticProb(F-statistic)7.4549520.3127410.1007860.3324387.6545080.000032ProbabilityProbability0.0612770.072293Model 4.2White Heteroskedasticity Test:F-statisticObs*R-squared2.07762114.38385Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 03/11/10 Time: 20:59Sample: 1 49Included observations: 49VariableCoefficientStd. Errort-StatisticProb.CEDUCEDUC^2EXPEREXPER^2AGEAGE^2GENDERRACE0.017212-0.0125290.001869-0.0041560.0002200.002688-3.36E-050.016037-0.0306710.1985940.0231320.0016770.0059990.0002760.0080609.08E-050.0214460.0215080.086668-0.5416621.114506-0.6927980.7962910.333528-0.3697930.747803-1.4260270.93140.59110.27170.49240.43060.74050.71350.45900.1616R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodDurbin-Watson stat0.2935480.1522580.0618520.15302671.811681.983430Mean dependent varS.D. dependent varAkaike info criterionSchwarz criterionF-statisticProb(F-statistic)80.0506920.067177-2.563742-2.2162652.0776210.061277a)Write the estimated regression model in model 4.1 and explain the meaning of the slopecoefficients on EDUC and EXPER.b)In model 4.1, define the reference (base) group.c)Write the estimated regression models in model 4.1 for the group of black female and thegroup of white male.d)Carry out the White test (Model 4.2 – at 5% significance level) for heteroscedasticity bycompleting the following steps:-State the null hypothesis-Write down the test equation-Indicate the test statistic value-ConclusionH0: 1 = cNotes:H1: 1 ct stat =b1 c~ t nkSE (b1 )When df > 30, uset(0.10,df) -1.282 , t(0.90,df ) 1.282t(0.05,df) -1.645 , t(0.95,df ) 1.645t(0.025, df) -1.96, t(0.975, df) 1.96t(0.01, df) -2.326, t(0.99, df) 2.326t(0.005, df) -2.576, t(0.995, df) 2.576