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Marietta College

Spring 2011

Econ 420: Applied Regression Analysis

Dr. Jacqueline Khorassani

Week 1

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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?

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ODE

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

ERT

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

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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.

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Before Thursday1. Study the course contract

available at http://be.marietta.edu/community/khorassj/

2. Purchase the book and the statistical software (EViews)

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Before Thursday

3. Download EViews in your computer5. Study the EViews booklet6. Study Chapter 1

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On Thursday

• Expect ICA on– Course contract– Chapter 1

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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.

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Grading

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

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Tentative Course Outline• All the chapters in the right order

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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 with1. Using a sample of observations to estimate relationships

between two or more variables. Example?

2. confronting theories with facts and testing hypotheses involving behavior of variables.

3. predicting the behavior of variables.

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Thursday, January 12• All assignments carry 20 points.

About 1 hour tutorship in economics

• Who was interested again?

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Asst 1 (Teams of 2)1. What is regression analysis? 2. Describe the 3 major tasks that regression

analysis allows the researcher to perform. 3. When will the study guide for this class be

posted online?

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• 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

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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

– X2i is 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 X2i on Yi. ß2 is another slope coefficient.

– єi is the stochastic (random) error term on of individual i

– the coefficients, β0 and β1, and β2 are the same for all individuals and need to be estimated

– the values of Y, Xs, and ε differ across observations

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Yi = β0 + β1 X1i + β2 X2i + єi

(i = 1, 2, 3,…N)

• Two components in the above regression equation 1. deterministic component (β0 + β1 X1i + β2 X2i )2. 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 given Xs• E(Yi|X1i & X2i) = β0 + β1 X1i + β2 X2i • 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)

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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

1. The measurement errors2. The effects of other factors on GPA3. The effect of choosing a wrong functional form• In our example the relationship between hours of

study (X1) and GPA may be non linear

4. The effects of random factors

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But we expect on average this error to be zero

• While the true equation is • Yi = β0 + β1 X1i + β2 X2i + єi

• Our expected (average—error free)equation is• E(Yi /X1i& X2i) = β0 + β1 X1i + β2 X2i

• Now if we hold X2i constant, we can show the relationship between E(Yi) and X1i via a linear line

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• 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.

Yi = β0 + β1 X1i + β2 X2i + єi

(i = 1, 2, 3,…N)

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Theoretical regression line given a constant X2i

X1i

Yi

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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!!)

ß0=1.0

Slope = ß1 = 0.2

E(Yi) = β0 + β1 X1i

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But we know that there are some errors

X1i

Yi

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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

E(Yi) = 1 + 0.2 X1i

*Yang

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E(Y Yang)=2

Y Yang=3

єYang

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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?

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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

Asst 2: Due Tuesday in class

1. #3, Page 25• Remember that you must type your answers.

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