Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals

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Chapter 5

• Regression with a Single Regressor Hypothesis
  Tests and Confidence Intervals

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Regression with a Single Regressor Hypothesis
Tests and Confidence Intervals(SW Chapter 5)
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But first a big picture view (and review)
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Object of interest ?1 in,
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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,
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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
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OLS regression reading STATA output
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Summary of Statistical Inference about ?0 and ?1
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Regression when X is Binary(Section 5.3)
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Interpreting regressions with a binary regressor
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Summary regression when Xi is binary (0/1)
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Heteroskedasticity and Homoskedasticity, and
Homoskedasticity-Only Standard Errors (Section
5.4)
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Homoskedasticity in a picture
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Heteroskedasticity in a picture
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A real-data example from labor economics
average hourly earnings vs. years of education
(data source Current Population Survey)
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The class size data
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So far we have (without saying so) assumed that u
might be heteroskedastic.
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What if the errors are in fact homoskedastic?
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We now have two formulas for standard errors for

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Practical implications
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Heteroskedasticity-robust standard errors in
STATA
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The bottom line
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Some Additional Theoretical Foundations of OLS
(Section 5.5)
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Further Questions
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The Extended Least Squares Assumptions
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Efficiency of OLS, part I The Gauss-Markov
Theorem
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The Gauss-Markov Theorem, ctd.
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Efficiency of OLS, part II
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Some not-so-good thing about OLS
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Limitations of OLS, ctd.
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Inference if u is Homoskedastic and Normal the
Student t Distribution (Section 5.6)
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Practical implication
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Summary and Assessment (Section 5.7)