Econ103_Spring11_lec6-1

# Econ103_Spring11_lec6-1 - ECON 103 Lecture 6 Simple...

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ECON 103, Lecture 6: Simple Regression and testing Maria Casanova April 14 (version 0) Maria Casanova Lecture 6

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1. Introduction We consider the linear regression model Y i = β 0 + β 1 X i + u i We have seen that, when ˆ β 0 and ˆ β 1 denote the OLS estimator of β 0 and β 1 , respectively, and n is large, ˆ β 0 N ± β 0 , Var ( ˆ β 0 ) ² ˆ β 1 N ± β 1 , ( ˆ β 1 ) ² This implies that ˆ β 0 - β 0 SE ( ˆ β 0 ) N (0 , 1) and ˆ β 1 - β 1 SE ( ˆ β 1 ) N (0 , 1) Maria Casanova Lecture 6
1. Introduction 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 Maria Casanova Lecture 6

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2. Hypothesis Testing Steps of hypothesis testing for a parameter of the linear regression model: 1 Formulate the null hypothesis (e.g. H 0 : β j = 0) 2 Formulate the alternative hypothesis (e.g. H 1 : β j 6 = 0) 3 Specify the signiﬁcance level 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. Maria Casanova Lecture 6
2. Hypothesis Testing 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 the null hypothesis that β 1 = 0, we often say that β 1 is statistically signiﬁcant”, or “ β 1 is positive/negative and statistically signiﬁcant. Maria Casanova Lecture 6

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2. Hypothesis Testing Example: Does class size have an eﬀect on test scores?
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Econ103_Spring11_lec6-1 - ECON 103 Lecture 6 Simple...

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