Econ103fall10lec5

# Econ103fall10lec5 - Introduction Hypothesis Testing...

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Unformatted text preview: Introduction Hypothesis Testing Confidence Intervals Binary Independent Variable Econ 103, UCLA, Fall 2010 Introduction to Econometrics Lecture 5: Simple Regression and Testing Sarolta Laczó October 7, 2010 Introduction Hypothesis Testing Confidence Intervals Binary Independent Variable Introduction We consider the linear regression model Y i = β + β 1 X i + u i We have seen that, when ˆ β and ˆ β 1 denote the OLS estimator of β and β 1 , respectively, and n is large, ˆ β ∼ N β ,V ar ( ˆ β ) ˆ β 1 ∼ N β 1 ,V ar ( ˆ β 1 ) This implies that ˆ β- β SE ( ˆ β ) ∼ N (0 , 1) and ˆ β 1- β 1 SE ( ˆ β 1 ) ∼ N (0 , 1) Introduction Hypothesis Testing Confidence Intervals Binary Independent Variable Introduction/2 Outline: Hypothesis testing (with class size - test scores example) Critical values p-values 2-sided and 1-sided tests Confidence intervals Binary independent variable Interpretation with advertising campaigns example Introduction Hypothesis Testing Confidence Intervals Binary Independent Variable Hypothesis Testing/1 Steps of hypothesis testing for a parameter of the linear regression model: 1 Formulate the null hypothesis (e.g. H : β j = 0 ) 2 Formulate the alternative hypothesis (e.g. H 1 : β j 6 = 0 ) 3 Specify the level of significance α (e.g. α = 5% ) 4 Calculate the actual value of the decision variable, called t-statistic . 5 Compute the critical values z α/ 2 and z 1- α/ 2 . 6 Decide whether you can or cannot reject the null hypothesis. Introduction Hypothesis Testing Confidence Intervals Binary Independent Variable Hypothesis Testing/2 We could also test whether β 1 = 5 , or 2, or any other number. However, testing the hypothesis that β 1 = 0 is somewhat special, because it is essentially a test of whether or not X i has any effect on Y i . When we can reject this special null hypothesis that β 1 = 0 , we often say that “ β 1 is statistically significant”, or “ β 1 is positive/negative and statistically significant. ” Introduction Hypothesis Testing Confidence Intervals Binary Independent Variable Hypothesis Testing/3 Example: Does class size have an effect on test scores?Example: Does class size have an effect on test scores?...
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Econ103fall10lec5 - Introduction Hypothesis Testing...

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