ECON 497 Practice MidtermPage 1 of 13

ECON 497: Economic Research and ForecastingName:______

Spring 2005 Bellas

Practice Midterm

You have three hours and twenty minutes to complete this exam. Answer all questions, and explain your answers. Fifty points total, points per part indicated in parentheses.

1. Linear regression involves estimating a linear relationship between one or more independent or explanatory variables and a dependent variable. Imagine that such a relationship has been estimated between the rate of return (in percentage points) on a company’s stock and the following explanatory variables:

concentration of the industry in which the firm operates (CONCi)

total annual revenue of the company in $1,000s (REVi)

a technology industry dummy variable (TECHi)

The estimated equation is:

RORi = -8 + 0.03*CONCi + 0.01*REVi + 1.4*TECHi

A. Calculate the predicted rate of return for a company operating in an industry with concentration of 100, which has revenues of $1,000,000 and is not a technology company. (1)

B. What is the interpretation of the coefficient on the technology industry dummy? (1)

C. Comment on the application of this model to a company with revenues of $100,000,000. (1)

2. Dummy variables take the value of 0 or 1 and allow qualitative factors to be represented in linear regression. In addition, interactive or slope dummies allow the effects of a second variable to vary from one qualitative group to another. For purposes of this question, imagine that the amount of time in minutes (Ti) it takes a person to complete a marathon (a 26.2 mile run) has been regressed on the participant’s age (Ai) and gender (indicated by a male dummy Mi) according to the following models:

i.

ii.

iii.

Regression results showed positive values for β0 and β1 and negative values for β2 in all three models.

A. Imagine that you were to graph the predicted time against age based on the results of the first model (model i.). Show what this would look like. (1)

B. Imagine that you were to graph the predicted time against age based on the results of the second model (model ii.). Show what this would look like. (1)

C. What would it mean if the estimated coefficient on β3 were positive and significant? (1)

D. Imagine that the estimated coefficients in the second model (model ii.) were

Ti = 190 + 1.5*Ai – 18.0*Mi

Calculate what the estimated coefficients would be if the male dummy were replaced with a female dummy. (1)

3. What would an economics class be without assumptions? This is especially true in an econometrics class because the basic regression model, conversationally known as ordinary least squares (OLS to its friends) relies on seven classical assumptions. If these assumptions are satisfied, OLS is the best linear unbiased estimator (BLUE) that can possibly exist. Without them, it is not.

A. One assumption is that the error term has constant variance. What is the eight-syllable term given to violation of this assumption? (1)

B. Another assumption is that no explanatory variable is a perfect linear function of any other explanatory variable(s). What is the eight-syllable term given to the violation of this assumption? (1)

C. A third assumption is that observations of the error term are uncorrelated with each other. What is the seven-syllable term given to the violation of this assumption? (1)

4. In a regression equation, there is a left hand side variable, usually known as the dependent variable or Yi, and the right hand side variable(s), usually known as the independent, explanatory or the Xi’s. In a sentence, explain the difference between the X’s in a regression being truly independent or merely explanatory and use the term “endogenous” in your explanation. (2)

5. One linear regression hypothesis test that all regression packages do is an F-test of the explanatory power of the model.

A. What is the null hypothesis of this test? (2)

B. If you get a p-value (known in SPSS as a SIG. value) of 0.497 for this F-test, what does this imply about the explanatory power of your model? (2)

C. If you get a p-value (known in SPSS as a SIG. value) of 0.007 for this F-test, what does this imply about the explanatory power of your model? (2)

6. As nice as the F-test is, the thing that most folks are really interested in is the t-test of significance of the estimated coefficients.

A. What is the null hypothesis of this test? (2)

B. If you get a p-value of 0.001 for this t-test, what does this imply about the estimated coefficient on the variable in question? (2)

7. Here is some totally fake SPSS output. Calculate the correct values for the blanks.

ANOVA

Model / Sum of Squares / df / Mean Square / F / Sig.
Regression
Residual
Total / 1800
BLANK A
3000 / 2
98
100 / 579
928 / 8.635 / 0.000

coefficients

Model / B / Std. Error / Standardized Coefficient
Beta / t / Sig.
(Constant)
X1
X2 / 27.00
3.00
BLANK E / 3.00
BLANK D
2.00 / 0.385
0.477 / BLANK B
2.00
0.50 / BLANK C
0.048
0.563

A. (2)

B. (2)

C. (2)

D. (2)

E. (2)

F. Calculate the R2 for this regression. (2)

8. One of my favorite things about the Studenmund text is his four criteria for determining if an explanatory variable should be added to a regression. Consider the following output from a regression of income on a person’s sex, age and (in the second version) a dummy variable for whether or not they live in a metro area.

Discuss whether or not the METRO variable should be included in the regression based on Studenmund’s four criteria. (2)

9. Imagine that you’re regressing the amount of time (in seconds) it takes a car to accelerate to 100 MPH (S) on the horsepower rating (H) of its engine. Offer an interpretation of the coefficient on horsepower under the following models.

A. Si = 60 – 0.007*Hi (2)

B. Si = 58 – 0.3*LN(Hi) (2)

10. Imagine that you get the following regression output:

Model Summary

Model / R / R Square / Adjusted
R Square / Std. Error of
the Estimate
1 / 0.992 / 0.984 / 927.63

coefficients

Model / B / Std. Error / Standardized Coefficient
Beta / t / Sig.
(Constant)
X1
X2 / 27.00
3.00
8.25 / 0.365
0.647
0.198

A. What problem do you likely have? (2)

B. What options are available for further detection of this problem? (2)

C. What should you do to address this problem in your regression? (2)

11. Imagine that you’re doing a regression in which household consumption is the dependent variable and household income is one of the explanatory variables.

A. Explain why you might find heteroskedasticity in this model. (2)

B. Explain how you might change the model to eliminate the heteroskedasticity. (2)