Potential Questions for First Test AGEC 317 - OLS



AGEC 317

Spring 2003

Do your own work. You can use a calculator and your 8½ x 11 inch cheat sheet. No other books, papers, notes, etc. can be used. Use the points as a guide for your time. Cheating on this examination will result in the recommendation of an “F” for the class.

Short Answer - answer as concisely as possible - 5 points

1. Let p(t) represent the price of a share of stock of a corporation at time t. What does the following statement tell us about the signs of the first and second derivatives of p(t)? The price of the stock is close to bottoming out.

2. Matrix W is a matrix of dimension n x k. What is the determinate of the matrix, W’W, if the relationship[pic]holds for all rows in W? What is the implication of this result in terms of OLS regression, if matrix W is the X matrix?

3. What two criteria discussed in class must be met before the adjusted R2 from two are more equations can be compared?

4. You have estimated a relationship between x1, x2, and y using OLS in which the F-statistic testing for the significance of a linear relationship between x1, x2, and y is rejected. Should you conclude that x1 and x2 cause y? Why or why not?

5. In Excel, how do you go about running regressions? Where is the regression package located and what ranges you must change to run a regression?

6. Graphically, show and explain in words, what is meant by an efficient estimator?

Longer Answer - use point totals for time allocation

8 points

7. Find the total differential for the following utility function, [pic]where x and z are consumable goods, a, b, and c are parameters of the utility function. Give the economic interpretation of the total differential.

10 points

8. Give and explain the assumptions necessary to derive the OLS estimator.

9. Besides the assumptions necessary to derive the OLS estimator, explain any necessary additional assumption(s):

a) to show the OLS estimator is an unbiased estimator,

b) to obtain the variance for the estimated coefficients, and

c) to perform statistical tests?

10. Answer the following questions, using the attached Excel printout.

The model estimated is [pic].

a) What is the interpretation of the coefficient associated with x2 in this model?

b) What is the null and alternative hypothesis associated with the t-statistic associated with x2?

c) Graphically, illustrate the meaning of the p-value associated with the t-statistic for x3? At an α level of 0.05, do you reject or fail to reject the t-test?

15 points

11. Explain the Gauss-Markov theorem. That is, what does BLUE stand for and explain each component of BLUE. What is the importance of BLUE?

20 points

12. Use the following equation and data to answer the following questions. Model to be considered is[pic]. You have the following two observations on y, [pic].

a) Derive the OLS estimator for [pic]. If you cannot derive the OLS estimator, you can hand in your test at this point and the derived estimator will be handed out to you for use in answering questions (b) and (c).

b) Calculate SST, SSE, and SSR for the equation. Why or why not does SST = SSR?

c) Calculate the R2 for the equation. Intuitively, why does R2 equal the value you calculated (do not give a mathematical answer)?

|SUMMARY OUTPUT | | | | | | |

| | | | | | | |

Multiple R |0.83258402 | | | | | | | |R Square |0.69319616 | | | | | | | |Adjusted R Square |0.65484568 | | | | | | | |Standard Error |5.28882115 | | | | | | | |Observations |19 | | | | | | | | | | | | | | | | |ANOVA | | | | | | | | |  |df |SS |MS |F |Significance F | | | |Regression |2 |1011.190775 |505.595388 |18.0752928 |7.8503E-05 | | | |Residual |16 |447.546067 |27.9716292 | | | | | |Total |18 |1458.736842 |  |  |  | | | | | | | | | | | | |  |Coefficients |Standard Error |t Stat |P-value |Lower 95% |Upper 95% | | |Intercept |0.20456689 |2.233527617 |0.09158915 |0.92816138 |-4.5302991 |4.93943285 | | |x2 |0.74764015 |0.320790666 |2.33061692 |0.03318266 |0.06759447 |1.42768583 | | |x3 |0.5626232 |0.283350348 |1.9856097 |0.06448911 |-0.0380526 |1.16329897 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

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