Lecture7

# Lecture7 - Lecture 8 Hypothesis Testing Econ 444 Winter...

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Unformatted text preview: Lecture 8 : Hypothesis Testing Econ 444, Winter 2010 Feb 1, 2010 Some more examples of t-test ˆ Y i = 29 . 58 + 2 . 89 X i ( . 898 ) ( . 492 ) N = 25 , R 2 = . 79 Now test the following hypothesis : H : β 1 = 3 H A : β 1 , 3 Testing linear restrictions using t-test Consider the following regression equation : Y i = β + β 1 X 1 i + β 2 X 2 i + i (1) Till now we have only learned how to test conditions on single parameters. For example whether β 1 = 0 or not or whether β 1 = 1 or not, or whether β 2 = 0. What if we want to test something like : H : β 1 + β 2 = 3 H A : β 1 + β 2 , 3 Testing linear restrictions using t-test In previous example H : β 1 + β 2 = 3 is an example of linear restriction. We can test such conditions on β 1 , β 2 using t-test. The t-ratio in this case is : t = ˆ β 1 + ˆ β 2- 3 SE ( ˆ β 1 + ˆ β 2 ) Testing linear restriction using t-test What is SE ( ˆ β 1 + ˆ β 2 ) ? We need to learn following concept for that : If X and Y are two random variables then, Var ( X + Y ) = Var ( X ) + Var ( Y ) + 2 Cov ( X , Y ) and Var ( X- Y ) = Var ( X ) + Var ( Y )- 2 Cov ( X , Y ) where Cov(X,Y) is covariance between X and Y. So let us do an example of this. Suppose we have data on testSo let us do an example of this....
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Lecture7 - Lecture 8 Hypothesis Testing Econ 444 Winter...

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