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8/17/2019 Econometrics - Intro to Multiple Regression
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Chapter 6Chapter 6
Introduction to
Multiple Regression
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Outline
1. Omitted variable bias
2. Causality and regression analysis
3. Multiple regression and OLS4. Measures of fit
. Sampling distribution of the OLS estimator
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Omitted Variable Bias
(SW Section 6.1)
8/17/2019 Econometrics - Intro to Multiple Regression
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Omitted variable bias, ctd.
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Omitted variable bias, ctd.
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Omitted variable bias, ctd.
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Omitted variable bias, ctd.
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Te omitted !ariable bias "ormula#
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8/17/2019 Econometrics - Intro to Multiple Regression
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$igression on causalit% and
regression anal%sis
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Ideal Randomi&ed 'ontrolled
periment
• Ideal ! sub"e#ts all follo$ the treatment proto#ol % perfe#t#omplian#e& no errors in reporting& et#.'
• Randomized ! sub"e#ts from the population of interest are
randomly assigned to a treatment or #ontrol group (sothere are no #onfounding fa#tors)
• Controlled ! having a #ontrol group permits measuring thedifferential effe#t of the treatment
• Experiment ! the treatment is assigned as part of thee*periment! the sub"e#ts have no #hoi#e& so there is no+reverse #ausality, in $hi#h sub"e#ts #hoose the treatmentthey thin- $ill $or- best.
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Bac* to class si&e#
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Return to omitted variable bias
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Te +opulation Multiple Regression
Model (SW Section 6.,)
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Interpretation o" coe""icients in
multiple regression
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Te O-S stimator in Multiple
Regression (SW Section 6.)
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ample# te 'ali"ornia test score
data
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Multiple regression in ST/T/
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Measures o" 0it "or Multiple
Regression (SW Section 6.)
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SER and RMSE
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R , and 2
R
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R , and 2 ctd.2
R
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Measures of fit, ctd.
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Te -east S3uares /ssumptions "or
Multiple Regression (SW Section 6.4)
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/ssumption 51# te conditional mean o"
u gi!en te included X s is &ero.
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Te Sampling $istribution o" te
O-S stimator (SW Section 6.6)
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Multicollinearit%2 +er"ect and
Imper"ect (SW Section 6.7)
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Te dumm% !ariable trap
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Perfect multicollinearity, ctd.
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Imperfect multicollinearity
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Imperfect multicollinearity, ctd.