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Marietta College

Spring 2011

Econ 420: Applied Regression Analysis

Dr. Jacqueline Khorassani

Week 4

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Corrections

• Exam 1– Tuesday, February 10 8

• Exam 2– Tuesday, March 24 22

• Exam 3– Monday, April 25, 12-2:30PM

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Tuesday, February 1• My home page is moved tohttp://mcis.marietta.edu/community/khorassj/• Who went to the lecture on Sunday night?

– Summaries are due before 5 pm this Friday• Send them as an email attachment to me

– If you asked her a questions, write it down and give it to me today.

Return and discuss Asst 4

1. Use Eviews to estimate the coefficients in our classroom height – weight example; attach

a) the estimation output• Is the first thing you get after you estimate your

model (reports the estimated coefficients)b) the graph of actual weight, predicted weight and

the residualsc) Is Jackie above the estimated line or below it; why?

• Above, due to positive residual

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#5, Page 26

(a)The coefficients are not the same; different samples

(b) Equation 1.21 has the steeper slope (6.38 > 4.03) Equation 1.24 has the greater intercept (125.1 > 103.4)They intersect at 9.23 inches above 5 feet (162.3 pounds)

(c) Equation 1.24 misguesses by more than ten pounds on exactly the same 3 observations as Equation 1.21. But overall, 1.21 does better

(smaller residuals) predicting inside its own sample (no surprise!)

(d) Use an average of the two equationsCombine samples Use 1.24 because of bigger sample

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# 6, Page 26

(a) The percentage chance of making the putt decreases by 4.1 for each foot that the putt is longer (ignoring the effect of all other

relevant variables)(b) The equations are identical since ei = Pi –

P^i

(c) 42.6 percent, yes; 79.5 percent, no (too low); -18.9 percent, no (negative!).

(d) Relationship seems to be nonlinear

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Return Asst 5: estimate Ŷi= ^0+ ^1 Xi + ^2 Gi

Did R squared go up as you added G to your model?

Obs i Yi Xi Gi Obs i Yi Xi Gi

1. Jackie 140 64 0 10. Tina 100 63 0

2. Seth 200 73 1 11. Yuan 136 72 1

3. Xi Ni 110 65 0 12. Mason 165 70 1

4. Nate 172 70 1 13. Steven 182 70 1

5. Sally 108 62 0 14. Mike 143 73 1

6. Linda 105 68 0 15. Yang 180 72 1

7. Aaron 266 77 1 16. Nick 178 73 1

8. Charlotte

125 64 0 17. Elliot 132 70 1

9. Phillip 155 70 1

Collect Asst 6

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1. # 4 , Page 592. # 6, Page 603. #7, Page 61

Chapter 3: Steps in Applied Regression Analysis (Exactly what some of you will do in Econ 421)

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1. Identify the question– What do you have interest in?– We are looking for cause and effect

relationships• An example of a perfect but useless

regression – Give me an example please!!!

2. Review the literature

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a) Theoretical literature will help you to Specify the model

Dependent and Independent Variables• How are they measured ?• Real/nominal variables?• Any dummy variables?• Don’t want any omitted variables• Don’t want extra (not needed) variables

Functional formLinear/non-linear

Hypothesize the expected signs of coefficients

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b) Review of empirical literature will help you to

• See what others have done –Their variables–Their functional forms–Their data sources–Their estimation methods–Their findings

3. Specify the model

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• Based on the review of literature• Not based on what increases R bar2

4. Hypothesize the expected signs of coefficients

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• Based on– Theoretical /empirical literature

• Note: You do this before you estimate the equation and see the estimated coefficients

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Cross Sectional or Time Series? Degrees of freedom Inspect the data

What are the units of measurements? Any outliers? Any values that don’t make sense?

Clean the data

6. Choose the method of estimation

• OLS? Or something else?• Test for underlying econometric

problems

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7. Estimate and evaluate the equation

a) Overall quality of estimation• Adjusted R squared• Other test: F- test

b) Test your hypotheses–T-test–F-test–Other tests

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8. Document the results

• Meanings & interpretations• Predictions• Policy recommendations• Shortcomings of the study• What should the future studies do?

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Asst 7: Due Thursday in class

1. #3, Page 852. #5, Page 87

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Thursday, February 3• Summaries of Sunday night lecture are due before

5 pm this Friday via an email attachment– If you asked her a questions, write it down and give it to

me today.• My home page is moved tohttp://mcis.marietta.edu/community/khorassj/• Exam 1

– Next Tuesday– Covers Chapters 1 through 3– Closed book and notes

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Data source for Exam 1• http://pearsonhighered.com/studenmund/

– Using Econometrics: A Practical Guide, 6/e Studenmund

– Data Sets– Chapter 2– Eviews– FINAID

• Save the data set in a workfile on your computer and bring your computer to class.

Return and discuss Asst 6

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1. # 4 , Page 592. # 6, Page 603. #7, Page 61

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# 4 , Page 59(a) Sum of squares residuals (RSS) are minimized with respect to

coefficients (beta hats)(b) R2 = 1 – RSS/TSS or

R2 = ESS/TSSIf R2 = 0, then RSS = TSS, and ESS = 0Your line does not predict the value of dependent variable neither better than nor worse than the mean dependent variableR2 < 0 is possible only if the constant term (intercept) is omitted That means that RSS>TSSYour line predicts the value of dependent variable worse than the mean dependent variableGraph

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c. Positived. We prefer Model T because it includes more

relevant variables Note: A higher R2 does not automatically mean that an equation is preferred.

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# 6, Page 60a. Positive & Positiveb. Maybe! c. One more hour of lecture = 1/25 = 0.04 (4% of classes)

One more hour of lecture will increase grade by 0.04 1.74= 0.07

One more of problem set = 1/50= 0.02 (2% of problem sets)One more hour of problem sets increases grade by 0.02 0.60= 0.01

so going to class pays off more.

d. 0.02 1.74 < 0.10 0.60, so doing problem sets pays off more. Since the units of variables can differ dramatically, coefficient size does not measure importance. If all variables are measured identically, then the size of the coefficient is a measure of importance.

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e. An R2 of 0.33 means that a third of the variation of student grades around their mean can be explained by attendance at lectures and the completion of problem sets.

This is about right!f. The most likely variable to add is measure of

student ability (IQ score, ACT score). We’d expect both R2 and R bar 2 to rise.

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a. Equation B is betterX4 is a theoretically sound variable for a campus track

X3 seems poorly specified because an especially hot or cold day would discourage fitness runners

b. The coefficient of an independent variable tells us the impact of a one-unit increase in that variable on the dependent variable holding constant the other explanatory variables in the equation. If we change the other variables in the equation, we’re holding different variables constant, and so the has a different meaning.

#7, Page 61

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Collect and discuss Asst 7

1. #3, Page 852. #5, Page 87

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#3, Page 85a. A male professor in this sample earns $817 more than

a female professor, holding constant the other independent variables in the equation.

b. A key point here is not to change expectations based solely on this result.

c. R is not a dummy variable because it takes on more than two values. For each additional year in rank, the ith professor’s salary will rise by $406, holding constant the other independent variables in the equation.

d. Yes, based on this sample.f. A measure of the quality of the professor

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#5, Page 87a. Positiveb. The best equation includes the actual traffic

data. But, since the traffic dummy variable is correlated with the actual traffic variable, it seems slightly better than Equation 3.5.

c. No! The theoretical underpinnings of the model are much more important. Of course, the higher Rbar2 is certainly a plus.