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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 Lacz October 7, 2010 Introduction Hypothesis Testing Confidence Intervals Binary Independent Variable Introduction We consider the linear regression model Y i = + 1 X i + u i We have seen that, when and 1 denote the OLS estimator of and 1 , respectively, and n is large, N ,V ar ( ) 1 N 1 ,V ar ( 1 ) This implies that  SE ( ) N (0 , 1) and 1 1 SE ( 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 pvalues 2sided and 1sided 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 : j = 0 ) 2 Formulate the alternative hypothesis (e.g. H 1 : j 6 = 0 ) 3 Specify the level of significance (e.g. = 5% ) 4 Calculate the actual value of the decision variable, called tstatistic . 5 Compute the critical values z / 2 and z 1 / 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 1 = 5 , or 2, or any other number. However, testing the hypothesis that 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 1 = 0 , we often say that 1 is statistically significant, or 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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 Spring '10
 Davis

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