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Chapter 5

- Regression with a Single Regressor Hypothesis

Tests and Confidence Intervals

Regression with a Single Regressor Hypothesis

Tests and Confidence Intervals(SW Chapter 5)

But first a big picture view (and review)

Object of interest ?1 in,

Hypothesis Testing and the Standard Error of

(Section 5.1)

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Formula for SE( )

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Summary To test H0 ?1 ?1,0 v. H1 ?1 ?

?1,0,

Example Test Scores and STR, California data

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Confidence Intervals for ?1(Section 5.2)

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A concise (and conventional) way to report

regressions

OLS regression reading STATA output

Summary of Statistical Inference about ?0 and ?1

Regression when X is Binary(Section 5.3)

Interpreting regressions with a binary regressor

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Summary regression when Xi is binary (0/1)

Heteroskedasticity and Homoskedasticity, and

Homoskedasticity-Only Standard Errors (Section

5.4)

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Homoskedasticity in a picture

Heteroskedasticity in a picture

A real-data example from labor economics

average hourly earnings vs. years of education

(data source Current Population Survey)

The class size data

So far we have (without saying so) assumed that u

might be heteroskedastic.

What if the errors are in fact homoskedastic?

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We now have two formulas for standard errors for

Practical implications

Heteroskedasticity-robust standard errors in

STATA

The bottom line

Some Additional Theoretical Foundations of OLS

(Section 5.5)

Further Questions

The Extended Least Squares Assumptions

Efficiency of OLS, part I The Gauss-Markov

Theorem

The Gauss-Markov Theorem, ctd.

Efficiency of OLS, part II

Some not-so-good thing about OLS

Limitations of OLS, ctd.

Inference if u is Homoskedastic and Normal the

Student t Distribution (Section 5.6)

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Practical implication

Summary and Assessment (Section 5.7)