6. Do these data provide enough evidence at the 1% significance level to conclude that the fina

04 Jun 6. Do these data provide enough evidence at the 1% significance level to conclude that the fina

Question

Question 1 (30 marks)

Multiple Choice

• Select the answer that is most appropriate and CIRCLE on the MULTIPLE CHOICE

ANSWER SHEET provided on page 10. Answers not shown on Multiple Choice Answer

Sheet, 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) The value of y, for each value of x, is y = ?1 + ?2x + e

b) The variance of the random error e is var(e)= ?

2

c) The covariance between any pair of random errors ei and ej is zero

d) 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 increases

b) it decreases

c) it does not change

d) cannot be determined without more information

3. For which alternative hypothesis do you reject H0 if |t| ?t (?/2,N-2)?

a) ?k = c

b) ?k ? c

c) ?k > c

d) ?k < c 4. In which case would testing the null hypothesis involve a two-tailed statistical test? a) H1: Incentive pay for teachers does affect student achievement b) H1: Higher sales tax rates does not reduce state tax revenues c) H1: Extending the duration of unemployment benefits does not increase the length of joblessness d) H1: Smoking does not reduce life expectancy ECON271/371, Trimester 1 2012 3 5. The overall regression F-statistic tests the null hypothesis that a) 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 is zero. d) the slope coefficient of the variable of interest is zero, but that the other slope coefficients are not. 6. When should a researcher consider transforming the explanatory variable in a simple linear regression model? a) when a data plot suggests there is a non-linear functional form b) to get a coefficient estimate with the sign predicted by economic theory c) to reduce the variation in the explanatory variable d) to maximize SSR 7. Heteroskedasticity 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 other explanatory variables b) var(yi.) = var(ei) = ? 2 c) E(yi) = ?1 + ?2xi2 + ?3xi3 + ……. + ?kxik, ?E(ei) = 0 d) cov(yi, yj) = cov(ei, ej) = 0; (i?j) 8. 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 x b) the elasticity of y with respect to x c) cannot be determined without more information d) the mean value of ln(y) when ln(x) = 0. ECON271/371, Trimester 1 2012 4 9. In the multiple regression model, the t-statistic for testing that the slope is significantly different from zero is calculated a) by dividing the estimate by its standard error. b) from the square root of the F-statistic. c) by multiplying the p-value by 1.96. d) using the adjusted R2 and the confidence interval. 10. When autocorrelation is present, which assumption of the linear regression model is incorrect? a) E(et)=0 b) var (et)=? 2 c) cov(et, es) =0, t?s d) 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 + e where Y is wage, Y0 is wage of someone with no education or experience, EDU is years of education and EXPER is experience in the field. If you suspect males earn higher wages than females and that the wage difference increases with education, how would you adjust the econometric model to estimate wages? a) include a binary variable for gender, MALE b) include an interaction term equal to MALE* EXPER c) include an indicator variable for MALE and one for FEMALE d) include a binary variable for MALE and an interaction term equal to MALE * EXPER 12. How 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 when all remaining variables are unchanged b) the magnitude by which xk varies in the model c) the amount of variation in y explained by xk in the model d) the number of variables used in the model. ECON271/371, Trimester 1 2012 5 13. A model estimated using a dataset with 65 observations generates the following results. Variable ? Std. Error t-statistic P>|t|

x2 -0.01264 0.005519 -2.28937 0.022

x3 0.595792 0.014482 41.13934 0.000

x4 1.124589 0.877192 1.282032 0.200

x5 0.323742 0.060709 5.332661 0.000

Constant 8.86016 1.766116 5.016749 0.000

If you want to test the hypothesis that ?3 =0.45, what is the test statistic from this sample?

a) 41.139

b) 10.067

c) 31.072

d) 0.000

14. Which 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 other

explanatory variables.

b) var(yi.) = var(ei) = ?

2

c) 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 effects

b) there is no difference in interpretation since each observation is scaled by the same

divisor

c) take the inverse of the natural logarithm of the coefficient to find marginal effects

d) They should only be used for hypothesis testing. Coefficient estimates from the unweighted,

original model should be used for prediction.

ECON271/371, Trimester 1 2012

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Question 2 (30 marks)

A professor investigated some of the factors that affect an individual student’s final grade in his

course. He proposed the multiple regression model y = ?0 + ?1×1 + ?2×2 + ?3×3 + e, where y is the final

mark (out of 100), x1 is the number of lectures skipped, x2 is 1 for male and is 0 otherwise, and x3 is

the mid-term test mark (out of 100). The professor recorded the data for 50 randomly selected

students. The computer output is shown below.

Dependent Variable: Y

Method: Least Squares

Date: 03/11/12 Time: 14:35

Sample: 1 50

Included observations: 49

Variable Coefficient Std. Error t-Statistic Prob.

C 41.6 17.8 2.337

x1 -4.18 1.66 -2.518

x2 -1.17 1.13 -1.035

x3 0.63 0.13 4.846

R-squared 0.300916 Mean dependent var

Adjusted R-squared S.D. dependent var

S.E. of regression 3716 Akaike info criterion

Sum squared resid 8688 Schwarz criterion

Log likelihood F-statistic 6.558

Durbin-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 model

is overall significant?

4. Do these data provide enough evidence to conclude at the 5% significance level that the final

mark and the number of skipped lectures are related?

5. Do these data provide enough evidence at the 5% significance level to conclude that the final

mark 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 final

mark and the mid-term mark are positively related?

ECON271/371, Trimester 1 2012

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Question 3 (20 marks)

1. Consider a regression model:

Dependent Variable: Y

Model 3.1:

Method: Least Squares

Date: 03/11/10 Time: 15:13

Sample: 1975:1 1990:4

Included observations: 64

Variable Coefficient Std. Error t-Statistic Prob.

C 25531.67 6606.085 3.864871 0.0003

X1 50.11645 22.97292 2.181544 0.0333

X2 630.4908 310.3327 2.031661 0.0469

X3 -44.38278 14.03021 -3.163371 0.0025

X4 -41.81233 73.74987 -0.566948 0.5730

X5 14.06459 47.52730 0.295927 0.7684

X6 -150.6795 39.30457 -3.833637 0.0003

R-squared 0.493523 Mean dependent var 2488.594

Adjusted R-squared 0.440210 S.D. dependent var 332.9220

S.E. of regression 249.0894 Akaike info criterion 13.97642

Sum squared resid 3536594. Schwarz criterion 14.21255

Log likelihood -440.2454 F-statistic 9.257019

Durbin-Watson stat 1.955138 Prob(F-statistic) 0.000000

Breusch-Godfrey Serial Correlation LM Test:

Model 3.2:

F-statistic 1.509310 Probability 0.224383

Obs*R-squared 1.679655 Probability 0.194970

Test Equation:

Dependent Variable: RESID

Method: Least Squares

Date: 03/11/10 Time: 19:20

Presample missing value lagged residuals set to zero.

Variable Coefficient Std. Error t-Statistic Prob.

C -623.1706 6596.300 -0.094473 0.9251

X1 -0.743301 22.87897 -0.032488 0.9742

X2 -49.84859 311.6085 -0.159972 0.8735

X3 -0.655310 13.97813 -0.046881 0.9628

X4 -8.068256 73.71570 -0.109451 0.9132

X5 -1.874936 47.34098 -0.039605 0.9685

X6 6.364603 39.47159 0.161245 0.8725

RESID(-1) 0.164068 0.133547 1.228540 0.2244

R-squared 0.026245 Mean dependent var -8.95E-12

Adjusted R-squared -0.095475 S.D. dependent var 236.9313

S.E. of regression 247.9839 Akaike info criterion 13.98107

Sum squared resid 3443778. Schwarz criterion 14.25093

Log likelihood -439.3944 F-statistic 0.215616

Durbin-Watson stat 1.914130 Prob(F-statistic) 0.980351

a) Carry out the Durbin-Watson test for first-order autocorrelation at the 5% significance

level.

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 regression analysis applied to time-series

data. What is the effect of a 1-unit increase in x in period t and (t+1)?

ECON271/371, Trimester 1 2012

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