## Question

1. Which of the following is not an assumption of the error term in the classical normal regression model?

A. zero correlation between the error and the independent variables

B. zero correlation between the error and the dependent variable

C. error has a mean of zero

D. error has a constant variance

E. error term follows a normal distribution

2. Suppose the least squares estimated regression model is given by:

Demand for Autos = 12.0 - 0.5* Price + 1.2*Income

Based on this estimated model an increase in Price and Income of 2 units is predicted to lead to:

A. a decrease in demand for Autos of 2.4 units

B. an increase of demand for Autos of 1.4 units

C. no change in the demand for autos

D. a decrease in demand for Autos of 1.4 units

E. an increase in demand for Autos of 0.4 units

3. Suppose the following regression model is estimated for the change in wages W as a function of the unemployment rate U:

W = .007 - 0.18*U -0.01*U 2

This implies that a decrease in the unemployment rate U is predicted to lead to:

A. a decrease in W

B. an increase in W

C. no change in W

D. initially an increase in W then a decrease in W

E. initially a decrease in W then an increase in W

4. Which of the following is a specification error in regression?

A. including a relevant independent variable

B. excluding an irrelevant independent variable

C. including an irrelevant independent variable

D. including the constant term

E. adopting the correct functional form

5. The SEE or SER statistic in the estimated Regression model always lies between

A. 0 and 1

B. -1 and 1

C. any negative value and 1

D. no restriction any value

E. 0 and infinity

6. Suppose the income variable is omitted in a demand for bus travel model. The sign of the bias for the estimated slope of the included price or fare variable is (assume that bus travel is an inferior good and that price and income are positively correlated)

A. negative

B. both positive and negative

C. neither positive nor negative since no bias is present

D. cannot be determined from information given

E. positive

7. In the log linear regression model the

A. slope is varying, elasticity is constant

B. slope and elasticity are both varying

C. elasticity is varying, slope is constant

D. slope and elasticity are both constant

E. none of the above

8. Suppose that the true model is given by:

Y = β0 + β1 X1 + β2 X2 + error

But the econometrician erroneously estimated the model:

Y = β0 + β1 X1 + error

Then the least squares estimate of β1 will be:

A. unbiased

B. best linear and unbiased

C. biased

D. unbiased but not have minimum variance

E. unattainable

9. Economic theory usually provides information on

A. which independent variables to include in a regression model

B. the functional form of the relationship between the dependent and independent variables

C. the expected signs of the slope parameters in the regression model

D. whether or not to include an error term in the regression model

E. all of the above

10. Given the Regression Model for Salary (Y):

Y = β0 + β1*X + β2*D + error

Where Y= House price

X = living area in square feet

D = 1 for house with central air

0 otherwise

The parameter β2 measures the:

A. the expected change in price for a house without central air

B. the relation between central air and price of house

C. whether the house has central air or not

D. the effect of an increase in living area on sale price of house

E. the difference in expected price of a house with central air and one without central airAnswer the following two questions based on the following estimated linear regression model for the demand for money:

M = 1.2 - 0.7* R + 1.4* Y

S. E. (0.3) (0.8)

N= 33 observations

Where M = demand for money

R = interest rate

And Y = income

11. Using the 5 % level of significance one concludes that:

A. both independent variables R and Y are statistically significant

B. both independent variables are statistically insignificant

C. only the interest rate variable is statistically significantD. only the income variable is statistically significant

E. cannot be determined from the information given.

12. Given the following information:

M = 15.0, R = 3.0 , and Y= 10.0

The forecast error for this period was:

A. 0.0

B. -2.9

C. -1.9

D. 3.9

E. none of the above

13. Suppose that in the simple regression model Y = β0 + β1* X + error:

The parameter β1 is found to be statistically insignificant then we can conclude that:

A. the economic theory that X causes Y is true

B. the economic theory that X cause Y is false

C. sample evidence supports the claim that X affects Y

D. the variable X is an important determinant of the variable YE. sample evidence does not support the claim that X affects Y

14. Which of the following statements is not true?

A. the sample mean is a measure of central tendency of a variable

B. the standard deviation is a measure of the variability of a variable

C. the histogram gives information on the sampling distribution of a variable

D. the correlation between two variables indicates whether there is a relation between them.

E. the scatter plot gives information on the relation between two variables in the sample

15. The first task in an applied regression analysis is to:

A. perform preliminary data analysis

B. estimate and evaluate the linear regression model

C. develop the theoretical regression model

D. hypothesize the expected signs of the coefficients in the model

E. use the model to carry out predictions of forecasts

PART B: THEORY REGRESSION

QUESTIONS

1. In the normal classical regression model the least squares estimators have desirable properties. More specifically the least squares estimators are unbiased and have minimum variance.

Illustrate the unbiased property of the least squares estimator by drawing two sampling distributions below. One for the least squares estimator β-hat and the other for a biased estimator say β-star. Be sure to carefully label your diagram.

2. One should always begin by specifying a linear in the variables model in a regression analysis study. True or False and give a reason for your choice?

3. State the two specification errors involving the selection of the independent variables in the Regression model. What are the consequences of each specification error for the estimated least squares regression model?

4. Distinguish between the dependent variable and the independent variable in a simple regression model.

PART C: APPLIED REGRESSION

QUESTIONS

1. An econometrician was interested in studying the starting salary of employees at a firm. The following Regression model was specified to study the determination of starting salaries:

SALARY (i) = β0 + β1*EDUC (i) + β2*EXP (i) + β3*DGEND (i) + ε (i)

where SALARY = starting salary of employee i in thousands of dollars

EDUC = education level of employee i in years

EXP = experience level of employee i in months

DGEND = 1 for male employee

0 for female employee

A) What is the name of the functional relation between the variables in this model?

B) Interpret the meaning of β3, the slope parameter for the DGEND variable in this model.

Using a sample on 474 individuals the above model was estimated using least squares estimates.

ESTIMATED LINEAR REGRESSION MODEL IS GIVEN BY:

SALARY (i) = -7.94 + 1.63*EDUC (i) + 0.012*EXP (i) + 3.45*DGEND (i)

s.e. (0.10) (0.003) (0.22)

R squared = 0.484 R Bar squared = 0.481 SEE = 5.67 (mean salary = 17.01)

C) Based on these Regression results are there any signs of the presence severe imperfect multicollinearity? Explain your answer.

D) Now suppose you are given the following additional information

CORR (EDUC, EXP) = -0.25

CORR (EDUC, DGEND) = 0.36 CORR (EXP, DGEND) = 0.17

VIF (EDUC) = 1.29

VIF (EXP) = 1.16

VIF (DGEND) = 1.24

Where CORR(X, Y) is the pair wise correlation between X and Y And VIF(X) is the variance inflation factor for the variable X

Are there any signs of severe imperfect multicollinearity now? Explain your answer using both indicators above.

The model was re-estimated without the DGEND variable obtaining the following results:

ESTIMATED LINEAR REGRESSION MODEL WITHOUT DGEND VARIABLE

SALARY (i) = -9.90 + 1.88*EDUC (i) + 0.016*EXP (i)

s.e. (0.097) (0.003)

R squared = 0.446 R Bar squared = 0.443 SEE = 5.87 (mean salary = 17.01)

E) Determine whether the variable DGEND should be included in the regression model by using each of the following four specification criteria. For each criterion:

i) Give the meaning of each criterion and explain how it is used to answer this question. ii) Apply the criterion to this specific example and state conclusions.

Economic theory

i)

ii)

t-test for hypothesis for sign i)

Adjusted R bar squared statistic

i)

ii)

Bias in other coefficient estimates

i)

ii)

F) Based on the findings in part E above can you determine whether the variable DGEND belongs in this model or not? Explain your answer.

2. Use the model with the DGEND variable in question 1 above to obtain the following predictions or forecasts: (Show work)

A) Starting Salary for a male with 15 years of education and 1 year of experience.

B) Starting Salary for a male with 14 years of education and 2 years of experience.

C) Based on the two forecasts above is the individual better off going to school for an additional year or joining the labour force? Explain your answer.

D) Is the Linear in the variables model an appropriate model in this case? Explain why or why not.

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SOLUTIONPart A

Q1)

Ans.

A. zero correlation between the error and the independent variables

Q2)

Ans.

B. an increase of demand for Autos of 1.4 units

Q3)

Ans.

D. initially an increase in W then a decrease in W

Q4)

Ans.

C. including an irrelevant independent variable...

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Solution.docx.