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Marietta College

Marietta College. Spring 2011 Econ 420: Applied Regression Analysis Dr. Jacqueline Khorassani. Week 1. Tuesday, January 11. Introduction Why are you in this class? Do you have the prerequisite for this course? Do you have a laptop? Major/minor?

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Marietta College

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

  2. Tuesday, January 11 • Introduction • Why are you in this class? • Do you have the prerequisite for this course? • Do you have a laptop? • Major/minor? • Are you planning to take Econ 421 next semester? • Any question for me?

  3. ODE • What is it? • Let’s go on line to find out • http://be.marietta.edu/student-activities/ode

  4. ERT • What is it? • Let’s go on line to find out http://www.economicroundtable.org/

  5. 1 hour tutorship in economics • You will hold office hours in Thomas 123 at least 3 hours a week. • Contact Dr. Delemeester and me for information on ECON 211/212 • Econ 211/212 students will come to you with questions • If interested, contact me.

  6. Before Thursday • Study the course contract available at http://be.marietta.edu/community/khorassj/ • Purchase the book and the statistical software (EViews)

  7. Before Thursday 3. Download EViews in your computer 5. Study the EViews booklet • Study Chapter 1

  8. On Thursday • Expect ICA on • Course contract • Chapter 1

  9. We will meet • in Thomas 223 on Tuesdays • Bring EViews software (laptops) to these classes • In Thomas 209 on Thursdays • Bring calculators to these classes • Always bring your book to class.

  10. Grading • Three Exams (20% each) = 60% • Participation = 5% • Assignments =35%

  11. Tentative Course Outline • All the chapters in the right order

  12. What is this course all about? • Regression analysis deals with the application of statistical methods to economics and other social and/or behavioral sciences. More broadly, it is concerned with • Using a sample of observations to estimate relationships between two or more variables. Example? • confronting theories with facts and testing hypotheses involving behavior of variables. • predicting the behavior of variables.

  13. Thursday, January 12 • All assignments carry 20 points.

  14. About 1 hour tutorship in economics • Who was interested again?

  15. 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?

  16. List the factors that affect a student’s GPA • A person’s GPA depends on hours of study, degree of intelligence, … what else? • Theoretical Regression Model (Equation) • Theoretical (Think of it as common sense relationship) • GPA = f ( hours of study, degree of intelligence, gender,…etc.) • GPA is the dependent variable • Hours of study and degree of intelligence are the Independent or explanatory variables

  17. More on the Theoretical Model • Yi = β0 + β1 X1i + β2 X2i + єi (i = 1, 2, 3,…N) • Where • N is the size of the population • There are really N equations, one for each individual • Yi is GPA of individual i (dependent variable) • X1i is hours of study of individual i • X2iis IQ score of individual i • β0 is read beta null (or beta zero) is a constant (or intercept coefficient) • β1 (reads beta 1) measures the effect of X1ion Yi. ß1 is also called a slope coefficient. • β2 (reads beta 2) measures the effect of X2ion Yi. ß2 is another slope coefficient. • єi is the stochastic (random) error term on of individual i • the coefficients, β0 and β1, and β2are the same for all individuals and need to be estimated • the values of Y, Xs, and ε differ across observations

  18. Yi = β0 + β1X1i + β2X2i + єi(i = 1, 2, 3,…N) • Two components in the above regression equation • deterministic component (β0 + β1X1i + β2X2i ) • stochastic/random component (єi) • Why “deterministic”? • the value of Y that is determined by a given values of Xs • Alternatively, the det. comp. can be thought of as the expected value of Y givenXs • E(Yi|X1i & X2i) = β0 + β1X1i + β2X2i • mean (or average) value of the Ys associated with a particular value of X • This is also denoted the conditional expectation (that is, expectation of Y conditional on X)

  19. Why is there an Stochastic Error (єi)? • We know that the relationship between Xs and Y is not always perfectly linear • Why not?...Because of • The measurement errors • The effects of other factors on GPA • The effect of choosing a wrong functional form • In our example the relationship between hours of study (X1) and GPA may be non linear • The effects of random factors

  20. But we expect on average this error to be zero • While the true equation is • Yi = β0 + β1X1i + β2X2i + єi • Our expected (average—error free)equation is • E(Yi /X1i& X2i) = β0 + β1X1i + β2X2i • Now if we hold X2i constant, we can show the relationship between E(Yi) and X1i via a linear line

  21. Yi = β0 + β1X1i + β2X2i + єi(i = 1, 2, 3,…N) • β1 measures the effect of one unit change in X1i on Yi, holding X2i constant. • β2 measures the effect of one unit change in X2i on Yi, holding X1i constant.

  22. Theoretical regression line given a constant X2i shows the theoretical relationship between the hours of study (X1) and GPA, holding X2 (degree of intelligence) constant and assuming that the error on average is zero. (Note: The theoretical line is not observable. But it is there in theory!!) Yi E(Yi) = β0 + β1X1i Slope = ß1 = 0.2 ß0=1.0 0 X1i

  23. But we know that there are some errors On average the error is zero But it is not zero for each individual For example, Yang studies 5 hours a week What is his expected GPA? 2.0 But we know that his true GPA is 3 єYang= E(Y Yang ) -Y Yang= 1 Yi E(Yi) = 1 + 0.2 X1i Y Yang=3 *Yang E(Y Yang)=2 єYang 0 X1i 5

  24. Regression Analysis • Uses sample data to estimate the position of the theoretical equation • That is to estimate β0 , β1, and β2 • A data set (sample) may be either Cross–Section • Observations on many individuals at a given point in time. • Or a data set (sample) may be Time-Series • Observations on one individual over time • What kind of data set do we use to estimate our equation? Why?

  25. In our case it is more feasible to use a cross section data set • the data set may consists of 100 individuals as of this point in time. • We collect information on each individual's • GPA • IQ • Hours of study

  26. Asst 2: Due Tuesday in class • #3, Page 25 • Remember that you must type your answers.

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