Lecture_4_Prof_Arkonac's_slides_(Ch_4)

Lecture_4_Prof_Arkonac's_slides_(Ch_4) - Linear Regression...

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Linear Regression with One Regressor (Intro to Econometrics) Lecture 4 Prof: Seyhan Arkonac, PhD Prolem Set 1 is due on Sept 21 st at the beginning of the class. 1
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TA Information: Naihobe Gonzalez E-mail: [email protected] Office Hours: Thurs 12-1 (Uris Library), Recitation: Thurs 11-11:50 (PUP 424) TA Information: Ju Hyun Kim E-mail: [email protected] Office Hours: Recitation: Fri 2:10-3PM(PUP 424), Office Hours: Fri 3:10- 4:10PM(Lehman) TA Information: WooRam Park E-mail: [email protected] Office Hours: Office hours : Thurs 2:00~3:00 IAB 1006A Recitation Thurs 3:10~4:00 IAB 403 TA Information: Ran Huo E-mail: [email protected] Office Hours: Recitation: Thursday 12:00-12:50 404IAB; Office Hour: Wednesday 1-2 1006A IAB TA Information: Shreya Agarwal E-mail: [email protected] Office Hours: Mon 12:30pm - 1:30 pm (Uris Library Common Area) Recitation: Fri 11:00am - 11:50am 2
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Stata sessions: Thursday 9/23, 11-11:50am, SCH 558 (Naihobe) Thursday 9/23, 12-12:50pm, SCH 558 (Ran) Thursday 9/23, 4:10-6pm, SCH 558 (WooRam) Friday 9/24, 2:10-3pm, SCH 558 (Ju Hyun) Every week starting 9/24 11-1150am SCH 558 (Shreya)
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4 Linear Regression with One Regressor Linear regression allows us to estimate, and make inferences about, population slope coefficients. Ultimately our aim is to estimate the causal effect on Y of a unit change in X – but for now, just think of the problem of fitting a straight line to data on two variables, Y and X .
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5 Estimation: How should we draw a line through the data to estimate the (population) slope (answer: ordinary least squares). What are advantages and disadvantages of OLS? Hypothesis testing: How to test if the slope is zero? Confidence intervals: How to construct a confidence interval for the slope? The problems of statistical inference for linear regression are, at a general level, the same as for estimation of the mean or of the differences between two means. Statistical, or econometric, inference about the slope entails:
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6 Linear Regression: Some Notation and Terminology (SW Section 4.1) The population regression line : Test Score = 0 + 1 STR 1 = slope of population regression line = Test score STR = change in test score for a unit change in STR Why are 0 and 1 “population” parameters ? We would like to know the population value of 1 . We don’t know 1 , so must estimate it using data.
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7 The Population Linear Regression Model – general notation Y i = 0 + 1 X i + u i , i = 1,…, n X is the independent variable or regressor Y is the dependent variable 0 = intercept 1 = slope u i = the regression error The regression error consists of omitted factors, or possibly measurement error in the measurement of Y . In general, these omitted factors are other factors that influence Y , other than the variable X
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8 This terminology in a picture : Observations on Y and X ; the population regression line; and the regression error (the “error term”):
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9 The Ordinary Least Squares Estimator (SW Section 4.2) How can we estimate 0 and 1 from data?
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This note was uploaded on 11/10/2011 for the course ECON 3142 taught by Professor Arkonac during the Spring '11 term at Columbia.

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Lecture_4_Prof_Arkonac's_slides_(Ch_4) - Linear Regression...

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