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Marietta College

Marietta College . Spring 2011 Econ 420: Applied Regression Analysis Dr. Jacqueline Khorassani. Week 2. Collect Asst 2: Due Tuesday in class. #3, Page 25. Return Asst 1 (Teams of 2). What is regression analysis?

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Marietta College

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  1. Marietta College Spring 2011 Econ 420: Applied Regression Analysis Dr. Jacqueline Khorassani Week 2

  2. Collect Asst 2: Due Tuesday in class • #3, Page 25

  3. Return Asst 1 (Teams of 2) • What is regression analysis? • Describe the 3 major tasks that regression analysis allows the researcher to perform. • When will the study guide for this class be posted online? • As promised, those of you who attended Econ Capstone Presentations last semester received 5 bonus points

  4. Let’s review what we know so far • Show the equation representing the theoretical relationship between GPA, hours of study and IQ scores of Marietta College students as of January 19, 2011. • Coefficients/ variables? • Stochastic/deterministic components? • What is the researcher’s job?

  5. The Estimated Equation • Ŷi= ^0+ ^1 Xi1 + ^2 Xi2 • Where • ^0 “beta hat zero” is the estimated constant term (β0, the true (theoretical) constant) • ^1 “beta hat one” is the estimated β1 • But what is Ŷi? • It is not the true GPA • It is the predicted (estimated) GPA • The true GPA (Yi) may be above or below the predicted GPA • Yi= ^0+ ^1 Xi1 + ^2 Xi2+ ei

  6. Let’s assume our estimated equation looks like this • Ŷi= 1+ 0.08Xi1 + 0.2Xi2 • Let’s draw the graph of GPA and hours of study (holding IQ constant) • Where are the observations in our sample? • Where is our fitted line? • The line shows the predicted (estimated) value of GPA at various hours of study and holding other factors (IQ) constant. • Are all observations on the line? • No, there are errors • To make sure we don’t mistake these errors for the stochastic errors in the theoretical equation, we call these errors RESIDUALS • ei measures the size of the residual on individual i • What is eiequal to? • Yi – Ŷi = ei

  7. What is the difference between the error terms and the residuals? • The stochastic error terms are • The residuals are • The stochastic error terms are not observable but the residuals are ; Why? • True regression equation (line) is theoretical (not observable) • Estimated regression equation (line) is observable • Residuals exist for the same reasons that errors exist plus • Residuals may be due to sampling and estimation errors /biases

  8. The OLS MethodChapter 2 • Chooses the intercept (β^0) and β^1 (slope coefficient) of the line (regression equation) in such a way that the sum of squared residuals (Σ ei2) is minimized • Why not just minimize the sum of residuals? • Positive errors will cancel the negative errors • The formulas for calculating β^0 and β^1 in a simple (2 variable equation) are given on Page 38 (Equations 2.4 & 2.5)

  9. Let’s think of the relationship between height and weight • Which variable is more likely to be the dependent variable? • Weight • Estimated model • Ŷi= ^0+ ^1 Xi • To estimate the model we collect cross sectional data set on height and weight in our classroom

  10. Asst 3: Use the following data set and the formulas on Page 38 to estimate ^0 and ^1 . Note: you must create a table similar to the one on Page 39.

  11. Thursday, January 20

  12. Return and discuss Asst 2 Question #3, Page 25 • positive • Negative (cross sectional sample) or first positive and then negative (time series sample) • positive • negative • ambiguous (since there is likely to be an accidental correlation) or no relationship • negative

  13. Collect and Discuss Asst 3 • The estimation results • The meaning of the coefficients • The omitted variables are ignored (not held constant) • What if we added another variable to our model? • Like what? • Would the coefficient on height change? • How would that change the meaning of the coefficient on height ? • The other included variables are held constant • The omitted variables are ignored (not held constant)

  14. Asst 3: Use the following data set and the formulas on Page 38 to estimate ^0 and ^1 . Note: you must create a table similar to the one on Page 39.

  15. Let’s use EViews to estimate this regression line • File • New • Workfile • Unstructured/undated • Observations 17 • ok

  16. In dialogue box type: data H W • Enter • Enter data using the keyboard • View • Graph • Scatter • Does the graph make sense to you? • Quick • Estimate equation • Type: W C H

  17. Let’s look at the graph of actual weight, predicted weight and the residuals • View • Actual fitted residual • Graph

  18. Asst 4: Due Tuesday in Class • Use Eviews to estimate the coefficients in our classroom height – weight example; attach • the estimation output • the graph of actual weight, predicted weight and the residuals • Is Jackie above the estimated line or below it; why? • # 5, Page 26 • # 6, Page 26

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