Econ 103A Midterm 2

1. In the equation, , is a(n) _____.
   a. independent variable
   b. dependent variable
   c. slope parameter
   d. intercept parameter

c

2. When testing the significance of a subset of regressors, the R² of the unrestricted model will always be:
   a. Greater than the R² of the restricted model.
   b. Less than the R² of the restricted model.
   c. Equal to the R² of the restricted model.
   d. It could be greater than, less than or equal to the R² of the restricted model.

a

3. The value of R² always _____.
   a. lies below 0
   b. lies above 1
   c. lies between 0 and 1
   d. lies between 1 and 1.5

c

4. If an independent variable in a multiple linear regression model is an exact linear combination of other independent variables, the model suffers from the problem of _____.
   a. perfect collinearity
   b. homoskedasticity
   c. heteroskedasticty
   d. omitted variable bias

a

5. Suppose the variable x₂ has been omitted from the following regression equation, y = β₀ + β₁x₁ + β₂x₂ + ε. β̂₁ is the estimator obtained when x₂ is omitted from the equation. The bias in β̂₁ is positive if _____.
   a. β₂ > 0 and x₁ and x₂ are positively correlated
   b. β₂ < 0 and x₁ and x₂ are positively correlated c. β₂ > 0 and x₁ and x₂ are negatively correlated
   d. β₂ = 0 and x₁ and x₂ are negatively correlated

a

6. High (but not perfect) correlation between two or more independent variables is called _____.
   a. heteroskedasticty
   b. homoskedasticty
   c. multicollinearity
   d. micronumerosity

c

7. Find the degrees of freedom in a regression model that has 36 observations and 7 independent variables.
   a. 29
   b. 5
   c. 28
   d. 13

c

8. Which of the following tools is used to test multiple linear restrictions?
   a. t test
   b. z test
   c. F test
   d. Unit root test

c

9. If R²ᵤᵣ = 0.6873, R²ᵣ = 0.5377, number of restrictions = 3, and n – k – 1 = 229, F statistic equals:
   a. 21.2
   b. 28.6
   c. 36.5
   d. 42.1

c

10. A variable is standardized in the sample:
    a. by multiplying by its mean.
    b. by subtracting off its mean and multiplying by its standard deviation.
    c. by subtracting off its mean and dividing by its standard deviation.
    d. by multiplying by its standard deviation.

c

11. Which of the following is true of dummy variables?
    a. A dummy variable always takes a value less than 1.
    b. A dummy variable always takes a value higher than 1.
    c. A dummy variable takes a value of 0 or 1.
    d. A dummy variable takes a value of 1 or 10.

c

12. The following simple model is used to determine the annual savings of an individual on the basis of his education.
    Savings = β₀ + β₁ Edu + u
    The variable ‘Edu’ takes a value of 1 if the person is educated and 0 if the person is uneducated.
    If β₁ > 0, _____.
    a. uneducated people have higher savings than those who are educated
    b. educated people have higher savings than those who are not educated
    c. individuals with lower income have higher savings
    d. individual with lower income have higher savings

b

13. The income of an individual in Budopia depends on his ethnicity and several other factors which can be measured quantitatively. If there are 5 ethnic groups in Budopia, how many dummy variables should be included in the regression equation for income determination in Budopia?
    a. 1
    b. 5
    c. 6
    d. 4

d

14. The quarterly increase in an employee’s salary depends on the rating of his work by his employer and several other factors as shown in the model below:
    Increase in Salary = β₀ + β₁Rating + β₂x₂ + ε
    The variable ‘Rating’ is a(n) _____.
    a. dependent variable
    b. ordinal variable
    c. continuous variable
    d. Poisson variable

b

15. Suppose that we include a dummy variable for male and a dummy variable for female in a regression. This will create a:
    a. Omitted variable bias problem
    b. Heteroskedasticity problem
    c. Multicollinearity problem
    d. Homoskedasticity problem

c

16. An omitted variable bias problem occurs when:
    a. We fail to include an independent variable that is not correlated with the dependent variable but is correlated with the main independent variable of interest.
    b. We fail to include an independent variable that is correlated with the main independent variable of interest and the error term.
    c. We fail to include the main independent variable of interest in the model.
    d. We fail to include an independent variable that is correlated with the error term but is not correlated with the main independent variable of interest.

b

17. A normal variable is standardized by:
    a. subtracting off its mean from it and multiplying by its standard deviation.
    b. adding its mean to it and multiplying by its standard deviation.
    c. subtracting off its mean from it and dividing by its standard deviation.
    d. adding its mean to it and dividing by its standard deviation.

c

18. Which of the following is a statistic that can be used to test hypotheses about a single population parameter?
    a. F statistic
    b. t statistic
    c. statistic
    d. Durbin Watson statistic

b

19. The general t statistic can be written as:
    a. (coefficient − hypothesized value) / standard error
    b. standard error / coefficient
    c. coefficient × standard error
    d. coefficient + standard error

a

20. Which of the following statements is true?
    a. When the standard error of an estimate increases, the confidence interval for the estimate narrows down.
    b. Standard error of an estimate does not affect the confidence interval for the estimate.
    c. The lower bound of the confidence interval for a regression coefficient, say âⱼ, is given by - [standard error × ( )].
    d. The upper bound of the confidence interval for a regression coefficient, say âⱼ, is given by + [Critical value × standard error ( )].

d

21. Smaller p-values indicate more evidence supporting:
    a. The alternative hypothesis
    b. The null hypothesis
    c. The need for more testing
    d. The quality of the data

a

22. A null hypothesis of H₀: β = 0 can be rejected at the 95% confidence interval if and only if:
    a. The 95% confidence interval contains zero
    b. The 95% confidence interval does not contain zero
    c. The null hypothesis is in the middle of the 95% confidence interval
    d. The sample size is sufficiently large (n≥30)

b

23. Which of the following are used to describe the goodness of fit for a model?
    a. The coefficient of the regression
    b. R²
    c. The standard error of the coefficient
    d. The constant

b

24. Imagine we have two separate models, Model 1 and Model 2. The R² for Model 1 is 0.8 and the R² for Model 2 is 0.4.
    a. Model 1 is a better model than Model 2
    b. Model 2 is a better model than Model 1
    c. R² is neither necessary nor sufficient for analysis to be useful

c

25. A null and alternative hypothesis are statements pertaining to:
    a. Sample parameters
    b. Sample statistics
    c. Population parameters
    d. It depends – In some cases it is population parameters, in others it is the sample statistics.

c

26. A statistical significance test that is based on a small sample may not produce a result that is statistically significant even if the true value of the coefficient is different from the value in the null hypothesis. Such a situation is:
    a. Power of the test
    b. Type I Error
    c. Type II Error
    d. Significance level of the test

c

27. Assume that the two-sided 95% confidence interval for the effect of a price on amount of beef purchased is between 0.30 and 0.38. Which of the following statements is NOT correct?
    a. We will reject the null hypothesis that this coefficient equals zero.
    b. There is less than a 2.5% chance that a coefficient higher than 0.38 would produce the coefficient we actually observe.
    c. There is a 95% chance that the true coefficient is between 0.30 and 0.38.
    d. There is a 95% chance that a random sample will produce a confidence interval that includes the true coefficient.

c

28. Please look at the equation below and pick the best answer
    a. β̂₁ will be positive if Y tends to be above its mean when X tends to be above its mean.
    b. The sign of β₁ will be the same sign as the denominator.
    c. Xᵢ can never equal X̄ for any observation
    d. β̂₁ will be positive if Xᵢ is always above X̄

a

29. When an independent variable is exogenous
    a. It is correlated with the error term
    b. It is not correlated with the error term
    c. It is correlated with the slope
    d. It is not correlated with the slope

b

30. An independent variable is endogenous if:
    a. It is correlated with another independent variable in the model.
    b. It is correlated with the error term.
    c. It is not correlated with the error term.
    d. If it is correlated with Y.

b

31. When using an auxiliary equation to help us think through an omitted variable bias question, if δ₁ is equal to zero then:
    a. We have an OVB problem and therefore need to include the variable
    b. The omitted variable is not correlated with the main independent variable, so no OVB problem
    c. We don’t care about δ₁ and instead focus on the error term
    d. Need more information

b

32. Which of the following are consequences of measurement error in the dependent variable?
    a. Smaller R²
    b. Biased coefficient estimates
    c. The bigger the measurement error, the bigger the variance of the error term
    d. None of the above

c

33. If the measurement error is in the independent variable, then
    a. No bias, it goes into the error term
    b. Bigger measurement error → bigger variance of error term
    c. Attenuation bias (coefficient closer to 0)
    d. Attenuation bias (coefficient larger than it should be)

c

34. In a case where there is multicollinearity in the model
    a. Independent variables have strong linear relationships
    b. Variance of estimates increases
    c. Leads to bias
    d. Both A and B
    e. Both A and C

d

35. What should we do when we have multicollinearity?
    a. Ignore it no matter what
    b. Drop some independent variables
    c. Test whether variables are jointly significant
    d. Add more independent variables

c

36. If we add more independent variables into the model:
    a. R² will decrease if variables shouldn’t be there
    b. R² will increase
    c. Adjusted R² will increase
    d. R² will be biased

b

37. Including irrelevant independent variables into the model:
    a. Will create bias
    b. Will reduce the precision of our estimates
    c. Will have no negative or positive effect
    d. Will lead to an increase in the error term

b

38. Which of the following are associated with larger omitted variable biases?
    a. The dependent variable is measured with error
    b. The relationship between included and excluded variables is weak
    c. The relationship between included and excluded variables is strong
    d. The relationship between the excluded variable and dependent variable is weak

c

39. The fitted values from a multivariate regression Yi = β₀ + β₁Xi + β₂Dummy + ei will be:
    a. Two parallel lines with slope β₂ and separated by β₁
    b. Two parallel lines with slope β₁ and separated by β₂
    c. Two lines with differing slopes separated by β₁
    d. Two lines with differing slopes separated by β₂

b

40. Consider the regression model:
    Wage = 10 + 2·Female + 3·Experience
    Female = 1 if female, 0 if male
    a. Females earn $2 more per year of experience
    b. Every female has wage $2
    c. Experience only affects females
    d. Females earn $2 more than males, holding experience constant

d

41. When dealing with categorical variables in multivariate regression, we:
    a. Include categorical variable directly
    b. Create dummies and include all
    c. Create dummies and include all but one
    d. Interact with continuous variable

c

42. Corruption = 10 − 0.1 GDP − 2.0 Democracy
    GDP = 50 (since $50k), Democracy = 1
    What is corruption?
    a. 5.0
    b. 8.5
    c. 3.0
    d. 6.0

c

43. Salary = 2000 + 500·College + 300·Female
    Male without college → College=0, Female=0
    a. 2300
    b. 2500
    c. 2000
    d. 2800

c

44. Salary = 2000 + 500·College + 300·Female
    Female with college → College=1, Female=1
    a. 2300
    b. 2500
    c. 2000
    d. 2800

d