Define dummy variable and give two examples

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Reference no: EM131132083

Practice Questions for the Final Exam:

Theoretical Part-

1. Define dummy variable and give two examples.

2. Analyze the three different types of data (cross-sectional, time series, panel data).

3. Define R2 and R-2. What is their important property? Show the relation between them and their differences. Analyze as much as you can.

4. (a) Analyze fully the assumption of "homoscedasticity" of a CLRM. Moreover, which are the differences with heteroscedasticity? (b) Analyze fully the assumption of specification bias and use an example to show your intuition.

5. State the CLRM (Classical linear Regression Model) Assumptions.

6. State the Gauss-Markov Theorem and provide full definitions of the characteristics of a BLUE estimator (unbiasedness, linearity, efficiency).

7. Analyze the procedure of the Maximum Likelihood (ML) Estimator for the following bivariate regression model: Yi = β1 + β2Xi + ui. Specify any advantages or disadvantages the ML estimator has over the OLS estimator. The formula for Log Likelihood is given as:

inL = -nlnσ2 - n/2 ln(2π) - 1/2 ∑ (Yi - β1 - β2Xi)22

8. You are given the following non-linear regression model

Y = β1X-β_2eu, where, Y: dependent variable, X: independent variable, e: exponent, u: error term, betas: coefficients. Make the necessary transformation/s so that the model can be estimated by using OLS method.

9. You are given the following two models:

(GPDI)^ =  -1026.5 + 0.30GDP

       se =  (257.58)          (0.04)

where GDPI and GDP are measured in billions of dollars

(GPDI*)^ = 0.94GDP*

        se  = (0.115)

where GDPI* and GDP* are the standardized versions of the variables GDPI and GDP.

Interpret the coefficient of GDP and GDP* with economic reasoning.

10. Analyze briefly the different reasons of doing hypothesis testing in a multiple regression model.

11. Discuss two types of specifications errors that we may have in a classical linear regression model. Use an example for each case.

11. Choose the correct answer.

i. The α in confidence interval given by Pr (βi^ - δ ≤ βi ≤ βi^ + δ) = 1 - α is known as:

a. Confidence coefficient

b. Level of confidence

c. Level of significance

d. Significance coefficient

ii. The 1 - α in confidence interval given by Pr (βi^ - δ ≤ βi ≤ βi^ + δ) = 1 - α is known as:

a. Confidence coefficient

b. Level of confidence

c. level of significance

d. Significance coefficient

iii. Standard error of an estimator is a measure of

a. Population estimator

b. Precision of the estimator

c. Power of the estimator

d. Confidence interval of the estimator

iv. For a regression through the origin, the intercept is equal to

a. 1

b. 2

c. 0

d. -1

v. Which of the following statements is correct?

a. Multicollinearity arises when explanatory variables are highly correlated with each other.

b. Multicollinearity can be identified by examining the pattern of correlations among explanatory variables

c. A high correlation between the dependent variables and a given independent variable is a sign of mulicollinearity.

d. All of the above are correct

e. Only (a) and (b) are correct

f. Only (b) and (c) are correct

Empirical Part-

Problem 1 - The table contains the ACT scores and the GPA for eight college students. GPA is based on a 4- point scale and has been rounded to one digit after the decimal.

Student

GPA

ACT

1

2.8

21

2

3.4

24

3

3.0

26

4

3.5

27

5

3.6

29

6

3.0

25

7

2.7

25

8

3.7

30

Obtain the estimates α0^ and α1^ in the linear regression model: (GPAi)^ = α0^ + α1^ACT

Problem 2 -

(I) The following equation is part of a nutrition-based efficiency wage model: Total calories Cals were regressed on the number of meals MG given to guests at ceremonies, the number of meals ME given to employees and the number of meals MO given to guests on other occasions:

Cals = β0 + β1MG + β2ME + β3MO +e         (Model A)

The expected sign of the coefficients are β1 > 0, β2 > 0, β3 > 0

You ran the regression in Eviews, by using OLS, for the period 1960-1999 and you obtained the following output:

Dependent Variable: CALS

Method: Least Squares

Included observations: 40 after adjustments

Variable

Coefficient

Std. Error         t-Statistic

 

C

27.59394

17.41539

MG

0.607160

0.157120

ME

0.092188

2.311452

MO

0.244860

0.011095

R-squared

 

Mean dependent var

Adjusted R-squared

0.989590

S.D. dependent var

19.53879

S.E. of regression

 

Akaike info criterion

 

Sum squared resid

143.0726

Schwarz criterion

 

Log likelihood

-82.24700

Hannan-Quinn criter.

 

F-statistic

 

Durbin-Watson stat

0.897776

a. Some of the standard errors and t-statistics of the coefficients are missing from the output. Calculate them (be careful about the signs). Remember that the Null Hypothesis is:

H0: βi = 0. Test in α = 5% significance level. Your t-critical is given as 2.03. Do you reject or fail to reject the Null?

b. Interpret the effect of MG and ME variables with economic reasoning.

c. The value of R2 is missing from the output. Calculate it.

d. The standard error of regression is not visible in the above output. Calculate it by using the relevant formula: σ^2 = ∑u^i2/n-k, where n is the number of observations and k is the number of parameters.

e. The F value (for overall significance) you obtained is missing. Calculate it and test it for 5% significance level. The Fcritical(5%,3,36) is given as 2.87. Note that we are testing jointly for all the coefficients, excluding the intercept.

 f. Calculate the 95% Confidence Intervals for the coefficients of MG and MO.

(II) You decide to re-specify Model A, by dropping variable MO. Your model becomes:

Cals = β'0 + β'1 MG + β'2 ME + ε  (Model B)

You run the model and you obtain the following output:

Dependent Variable: CALS

Method: Least Squares

Included observations: 40 after adjustments

Variable

Coefficient

Std. Error         t-Statistic

.

C

35.45670

 

 

MG

2.567990

 

 

ME

0.892676

 

 

R-squared

0.860390

Mean dependent var

 

Adjusted R-squared

0.852844

S.D. dependent var

19.53879

S.E. of regression

7.495264

Akaike info criterion

 

Sum squared resid

2078.622

Schwarz criterion

 

Log likelihood

-135.7692

Hannan-Quinn criter.

 

F-statistic

114.0122

Durbin-Watson stat

0.678483

a. We do not know which model is better performed between model A and model B. Which model is better in terms of model building? Make use of the Information Criteria to find out which model is better.

b. The output is problematic. The standard errors and the t-statistics are missing. Use the Wald Test to do Restriction Testing between models A and B. The Null Hypothesis is: H0: β3 = 0. The Fcritical is given as 4.11 and the X12 critical value is given as 3.841 (both for a 5% significance level). What can you conclude regarding the dropped variable MO?

Problem 3 - lnipt+1 = β0 + β1lnolt + β2lnrsrt + β3emplt + ut

The above linear regression model states that the industrial productivity (lnip) is positively affected by the stock market returns (lnrsr) and the employment ratio (empl) and negatively affected by the oil prices (lnlo). We are examining the USA market growth during the period 1960-1999.

In 1980 we have the introduction of the personal computer and we want to test whether there is any structural change after the year of 1980:

H0: There was no structural break (or change) after 1980

H1: There was a structural break (or change) after 1980

You get the following three outputs by doing the Chow Test.

Dependent Variable: LNIP

Method: Least Squares

Sample: 1960 1999

Included observations: 40

Variable

Coefficient

Std. Error         t-Statistic

Prob.

C

27.59394

1.584458          17.41539

0.0000

LNOL

-0.607160

0.157120        -3.864300

0.0004

LNRSR

0.092188

0.039883          2.311452

0.0266

EMPL

0.244860

0.011095          22.06862

0.0000

R-squared

0.990391

Mean dependent var

50.56725

Adjusted R-squared

0.989590

S.D. dependent var

19.53879

S.E. of regression

1.993549

Akaike info criterion

4.312350

Sum squared resid

143.0726

Schwarz criterion

4.481238

Log likelihood

-82.24700

Hannan-Quinn criter.

4.373414

F-statistic

1236.776

Durbin-Watson stat

0.897776

Prob(F-statistic)

0.000000

 

 

Dependent Variable: LNLIP

Method: Least Squares

Sample: 1960 1979

Included observations: 20

Variable

Coefficient

Std. Error         t-Statistic

Prob.

C

27.59882

2.433883          11.33942

0.0000

LNOL

-0.899693

0.297873        -3.020394

0.0081

LNRSR

0.181932

0.098121          1.854171

0.0822

EMPL

0.265328

0.058970          4.499342

0.0004

R-squared

0.913357

Mean dependent var

34.28700

Adjusted R-squared

0.897112

S.D. dependent var

6.199594

S.E. of regression

1.988596

Akaike info criterion

4.389592

Sum squared resid

63.27225

Schwarz criterion

4.588738

Log likelihood

-39.89592

Hannan-Quinn criter.

4.428467

F-statistic

56.22198

Durbin-Watson stat

1.116410

Prob(F-statistic)

0.000000

 

 

Dependent Variable: LNLIP

Method: Least Squares

Sample: 1980 1999

Included observations: 20

Variable

Coefficient

Std. Error         t-Statistic

Prob.

C

16.18376

3.874379          4.177124

0.0007

LNOL

-0.345689

0.136746        -2.527964

0.0224

LNRSR

0.151866

0.046860          3.240840

0.0051

EMPL

0.272712

0.008611          31.67100

0.0000

R-squared

0.993168

Mean dependent var

66.84750

Adjusted R-squared

0.991887

S.D. dependent var

13.68186

S.E. of regression

1.232329

Akaike info criterion

3.432546

Sum squared resid

24.29817

Schwarz criterion

3.631692

Log likelihood

-30.32546

Hannan-Quinn criter.

3.471421

F-statistic

775.3400

Durbin-Watson stat

1.665783

Prob(F-statistic)

0.000000

 

 

a. Explain the procedure of the Chow Tests, i.e the steps you have to take in order to make conclusions about the structural stability.

b. Calculate the Chow F-Statistic. According to the F statistic you just calculated do you reject or fail to reject the Null Hypothesis? What that means for your data? You are given that Fcritical(0.05, 4, 32) = 2.69.

Reference no: EM131132083

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