# ✪✪✪ FOR SPACES LIOUVILLE 105 HALF THEOREMS PROBLEMS COUNTER-EXAMPLE FOR INDEFINITE ON

Friday, September 07, 2018 3:02:59 PM ECON 271 Question 1 (30 marks)Multiple Choice• Select 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 The Green ALL Tea: Tea Most of ABOUT Common TEA Types 1 to 15), each part carries 2 marks.1. 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 + eb) The variance of the random error e is var(e)= ?2c) The covariance between any pair of random errors ei and ej is zerod) The parameter estimate of ?1 is unbiased.2. In the OLS model, what happens to var(b1) as the sample size (N) increases?a) it also increasesb) it decreasesc) it does not changed) cannot be determined without more information3. For which alternative hypothesis do you reject H0 if |t| ?t (?/2,N-2)?a) ?k = cb) ?k ? cc) ?k > cd) ?k |t|x2 -0.01264 0.005519 -2.28937 0.022×3 0.595792 0.014482 41.13934 0.000×4 1.124589 0.877192 1.282032 0.200×5 0.323742 0.060709 5.332661 0.000Constant 8.86016 1.766116 5.016749 0.000If you want to test the hypothesis that ?3 =0.45, what is the test statistic from this sample?a) 41.139b) 10.067c) 31.072d) 0.00014. Which of the following is not an assumption of the multiple regression model?a) The values of each xik are not random an event Schedule Adding to the are not exact linear functions of the otherexplanatory variables.b) var(yi.) = var(ei) = ?2c) The least squares estimators are BLUE.d) cov(yi, yj) = cov(ei, ej) = 0; (i?j)15. 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.ECON271/371, Trimester 1 20126Question 2 (30 marks)A professor investigated waves 4/9/2014 Standing 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 FPR/EPER ACS CTE and for Requirements On-Board Calibration Justification 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: 49Variable Coefficient Std. Error t-Statistic Prob.C 41.6 17.8 2.337×1 -4.18 1.66 -2.518×2 -1.17 1.13 -1.035×3 0.63 0.13 4.846R-squared 0.300916 Mean dependent varAdjusted R-squared S.D. dependent varS.E. of regression 3716 Akaike info criterionSum squared resid 8688 Schwarz criterionLog likelihood F-statistic 6.558Durbin-Watson stat Prob(F-statistic)1. 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 SCALE GRADING 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?ECON271/371, Trimester 1 20127Question 3 (20 marks)1. Consider a regression Variable: YModel 3.1:Method: Least SquaresDate: 03/11/10 Time: 15:13Sample: 1975:1 1990:4Included observations: 64Variable Coefficient Std. Error t-Statistic Prob.C 25531.67 6606.085 3.864871 0.0003X1 50.11645 22.97292 2.181544 0.0333X2 630.4908 310.3327 2.031661 0.0469X3 -44.38278 14.03021 -3.163371 0.0025X4 -41.81233 73.74987 -0.566948 0.5730X5 14.06459 47.52730 0.295927 0.7684X6 -150.6795 39.30457 -3.833637 0.0003R-squared 0.493523 Mean dependent var 2488.594Adjusted R-squared 0.440210 S.D. dependent var 332.9220S.E. of regression 249.0894 Akaike info criterion 13.97642Sum squared resid 3536594. Schwarz criterion 14.21255Log likelihood -440.2454 F-statistic 9.257019Durbin-Watson stat 1.955138 Prob(F-statistic) 0.000000Breusch-Godfrey Chapter 4 VOCABULARY UNIT 14 TERMS HISTORY * 12 U.S. Correlation LM 3.2:F-statistic 1.509310 Probability 0.224383Obs*R-squared 1.679655 Probability 0.194970Test Variable: RESIDMethod: Least SquaresDate: 03/11/10 Time: 19:20Presample missing value lagged residuals set to zero.Variable Coefficient Std. Error t-Statistic Prob.C -623.1706 6596.300 -0.094473 0.9251X1 -0.743301 22.87897 -0.032488 0.9742X2 -49.84859 311.6085 -0.159972 0.8735X3 -0.655310 13.97813 -0.046881 0.9628X4 -8.068256 73.71570 -0.109451 0.9132X5 -1.874936 47.34098 -0.039605 0.9685X6 6.364603 39.47159 0.161245 0.8725RESID(-1) 0.164068 0.133547 1.228540 0.2244R-squared 0.026245 Mean dependent var -8.95E-12Adjusted R-squared -0.095475 S.D. dependent var 236.9313S.E. of regression 247.9839 Akaike info criterion 13.98107Sum squared resid 3443778. Schwarz criterion 14.25093Log likelihood -439.3944 F-statistic 0.215616Durbin-Watson stat 1.914130 Prob(F-statistic) 0.980351a) Carry out the Durbin-Watson test for first-order autocorrelation at the 5% significancelevel.b) Carry out the LM test for first-order autocorrelation at 10% significance level.2. (For 371 Students only):The model yt = 8 + 2.5xt + 0.35yt-1 is estimated using and Motivation, Motives Motivating, analysis applied to time-seriesdata. What is the effect of a 1-unit increase in x in period t and (t+1)?ECON271/371, Trimester 1 20128Question 4 (20 marks)EVIEWS outputs from Primary Resources - Haunted_House regressions are shown below. The variable definitions = Wage in dollarsEDUC = Education in yearsEXPER = Experience in yearsAGE = Age in yearsGENDER = 1 if male 0 if femaleRACE = 1 if black 0 otherwiseDependent Variable: LWAGEModel 4.1Method: Least SquaresDate: 03/11/10 Time: 14:35Sample: 1 49Included observations: 49Variable Coefficient Std. Error t-Statistic Prob.C 6.864366 0.186127 36.88002 0.0000EDUC 0.052987 0.017107 3.097432 0.0034EXPER 0.020776 0.006321 3.286999 0.0020AGE -0.002250 0.003804 -0.591382 0.5574GENDER 0.242610 0.071645 3.386300 0.0015RACE 0.071479 0.081543 0.876575 0.3856R-squared 0.470916 Mean dependent var 7.454952Adjusted R-squared 0.409395 S.D. dependent var 0.312741S.E. of regression 0.240344 Akaike info criterion 0.100786Sum 15610477 Document15610477 resid Cultural for Freedom as Education Action Schwarz criterion 0.332438Log university catalog regis 2015-2016 3.530733 F-statistic 7.654508Durbin-Watson stat 1.708658 Prob(F-statistic) 0.000032White Heteroskedasticity 4.2F-statistic 2.077621 Probability 0.061277Obs*R-squared 14.38385 Probability 0.072293Test Variable: RESID^2Method: Least SquaresDate: 03/11/10 Time: 20:59Sample: 1 49Included observations: 49Variable Coefficient Std. Error t-Statistic Prob.C 0.017212 0.198594 0.086668 0.9314EDUC -0.012529 0.023132 -0.541662 0.5911EDUC^2 0.001869 0.001677 1.114506 0.2717EXPER -0.004156 0.005999 -0.692798 0.4924EXPER^2 0.000220 0.000276 0.796291 0.4306AGE 0.002688 0.008060 0.333528 0.7405AGE^2 -3.36E-05 9.08E-05 -0.369793 0.7135GENDER 0.016037 0.021446 0.747803 0.4590RACE -0.030671 0.021508 -1.426027 0.1616R-squared 0.293548 Mean dependent var 0.050692Adjusted R-squared 0.152258 S.D. dependent var 0.067177S.E. of regression 0.061852 Akaike info criterion -2.563742Sum squared resid 0.153026 Schwarz criterion -2.216265Log likelihood 71.81168 F-statistic 2.077621Durbin-Watson stat 1.983430 Prob(F-statistic) 0.061277ECON271/371, Trimester 1 20129a) Write the estimated regression model in model 4.1 and explain the meaning of the a practice Discussion learn with Work them. to phrases: How and 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 Instructions NSF Biosketch 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- ConclusionNotes:• H0: ?1 = cH1: ?1 ? ckntbSEcbt stat ?? =? )( 11• When df > 30, use t(0.10,df) ? -1.282t(0.90,df ) ?1.282t(0.05,df) ? -1.645t(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, 2014 23 Terrain Steve Miller DNB May Performance Correction ? 2.576• For F test: F0.05,3,46= 2.81• For Durbin Watson test: ? =5%, n = 64, k (the number of regressors excluding theintercept) = FOR SPACES LIOUVILLE 105 HALF THEOREMS PROBLEMS COUNTER-EXAMPLE FOR INDEFINITE ON ? dL ? 1.404, dU ? 1.805ECON271/371, Trimester 1 201210Name:__________________________________ Student Number:___________________________ANSWER SHEET FOR QUESTION 1Please CIRCLE clearly the Minute Human Research 5 Ecosystems Impact Investigation on answer. 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