Marietta College
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Transcript of Marietta College
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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
0
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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