Welcome to Econ 420 Applied Regression Analysis

1. Welcome to Econ 420 Applied Regression Analysis Study Guide Week Three Ending Tuesday, September 11 (Note: You must go over these slides and complete every task outlined here by noon on Wednesday September 14)

2. Assignment 1 • I will email you the graded assignment.

3. Answer Key to Assignment 1 • Question 1 • Use the data set on the next slide and the formulas on Page 8 (1-5 and 1-6) to estimated the coefficients β0^ and β1^ in the equation below W = β0^ + β1^ H • Make sure to show your work. • Do the estimated coefficients make sense to you? • What is the meaning of the estimated coefficients?

4. Here is our sample data on height and weight.

5. The estimated regression equations is • Wi= - 231 + 5.9 Hi • Here are the calculations:

6. Do the estimates make sense to you? What is the meaning of the estimated coefficients? • β0^ = - 232 is the intercept which measures the weight when the height is zero. This does not have useful information in it because • Zero height is impossible • The intercept captures the mean effect of all other excluded explanatory variables (such as calorie intake…..) on weight.,

7. Do the estimates make sense to you? What is the meaning of the estimated coefficients? • β1^ = 5.9 is slope of the line, it means, ignoring the effect of all other explanatory variables on weight, if the height increases by 1 inch, the weight will increase by 5.9 lb. • The sign (positive) makes sense. • The value may not make sense a lot because when we exclude the other explanatory variables from our equation, we can not hold them constant. And 5.9 may tend to in part capture the effect of excluded explanatory variables on weight.

8. 2. Question 5 on Page 15 • a. β1 is the true, theoretical value of the slope that expresses the relationship between X and Y. It is unobservable since we have a sample of data, and not all the data possible. β1^ is an estimate of β1 that is based on the sample data and comes from the regression process. • b. e is a theoretical error term that cannot be observed; it comes from measurement error, factors that influence the dependent variable that have not been included in the model, and random variation. e^ is an actual observation of the error term that comes from estimating the regression. It is also called the residual. • c. Y is the actual value of the dependent variable. Ŷ is the fitted or predicted value of the independent variable.

9. 3. Answer Question 8 on Page 15 • a. It means that the process finds estimates for the coefficients that minimize the squares of the errors. • b. It indicates that OLS minimizes the sum of the errors squared, not just the sum of the errors. • c. If you found the coefficient estimates by choosing values that minimize the sum of errors, you would not get the best regression line, because positive and negative errors would cancel each other out. That is why the errors must be squared.

10. Assignment 2 • This is an EViews assignment. • It is due before noon on Wednesday, September 12. • It has 20 points

11. To use EViews to estimate the coefficients of our height weight problem • Create and save an Excel spreadsheet • In boxes A1, B1 and C1 type obs, w, h respectively • Save your excel spreadsheet as book1 • Open EViews • Click on File, then new, then workfile • Choose undated • Set the start to 1 and end to 8

12. 5. Go to file then import then read excel 6. Find your excel file; make sure you choose excel as the option under file type 7. EViews will give you a window in which you will need to type w h (make sure there is a space between the two) 8. Now on the small window click on view and then show and then type w h in the box 9. EViews will give you a window with the values of w and h recorded in them. Check the values and make sure they are correct. 10. Now go on the top of the page and click on quick then estimate equation and then in the box type w c h (there should be a space between w, c , and h.) • We always type the dependent variable first, then c for constant or intercept (if you don’t’ type c, EViews will estimate an equation without an intercept.) and then the independent variable

13. 11. EViews will generate a table that summarizes the regression results.

14. Here is how your results should look • Dependent Variable: W • Method: Least Squares • Date: 09/09/07 Time: 08:15 • Sample: 1 8 • Included observations: 8 • Variable Coefficient Std. Error t-Statistic Prob. • C -231.1391 92.54581 -2.497565 0.0467 • H 5.879205 1.314659 4.472039 0.0042 • R-squared 0.769223 Mean dependent var 181.8750 • Adjusted R-squared 0.730760 S.D. dependent var 32.39681 • S.E. of regression 16.81016 Akaike info criterion 8.694162 • Sum squared resid 1695.489 Schwarz criterion 8.714023 • Log likelihood -32.77665 F-statistic 19.99913 • Durbin-Watson stat 1.128086 Prob(F-statistic) 0.004228

15. Press on shift and then highlight the output and copy it on a word document • Then • Identify the values on the EViews output that you understand • Identify the values on the EViews output that you don’t understand • Send the assignment to me before Wednesday, September 12 at noon as a word attachment to an email. • Make sure that under the subject of the email you put your last name, class, asst 2. • If it was me then the subject would have been • Khorassani,econ420,asst2

16. On Wednesday afternoon • Look for a new study guide on WebCt. • Study Guide 4