multreg2 - Economics 20 - Prof. Anderson 1 Multiple...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 20 - Prof. Anderson 1 Multiple Regression Analysis y = + 1 x 1 + 2 x 2 + . . . k x k + u 2. Inference Economics 20 - Prof. Anderson 2 Assumptions of the Classical Linear Model (CLM) So far, we know that given the Gauss- Markov assumptions, OLS is BLUE, In order to do classical hypothesis testing, we need to add another assumption (beyond the Gauss-Markov assumptions) Assume that u is independent of x 1 , x 2 ,, x k and u is normally distributed with zero mean and variance 2 : u ~ Normal(0, 2 ) Economics 20 - Prof. Anderson 3 CLM Assumptions (cont) Under CLM, OLS is not only BLUE, but is the minimum variance unbiased estimator We can summarize the population assumptions of CLM as follows y| x ~ Normal( + 1 x 1 ++ k x k , 2 ) While for now we just assume normality, clear that sometimes not the case Large samples will let us drop normality Economics 20 - Prof. Anderson 4 . . x 1 x 2 The homoskedastic normal distribution with a single explanatory variable E( y | x ) = + 1 x y f( y|x ) Normal distribution s Economics 20 - Prof. Anderson 5 Normal Sampling Distributions ( 29 [ ] ( 29 ( 29 ( 29 errors the of n combinatio linear a is it because normally d distribute is 0,1 Normal ~ that so , , Normal ~ s t variable independen the of values sample the on l conditiona s, assumption CLM Under the j j j j j j j sd Var- Economics 20 - Prof. Anderson 6 The t Test ( 29 ( 29 1 : freedom of degrees the Note by estimate to have we because normal) (vs on distributi a is this Note ~ s assumption CLM Under the 2 2 1 j----- k n t t se k n j j Economics 20 - Prof. Anderson 7 The t Test (cont) Knowing the sampling distribution for the standardized estimator allows us to carry out hypothesis tests Start with a null hypothesis For example, H : j =0 If accept null, then accept that x j has no effect on y , controlling for other x s Economics 20 - Prof. Anderson 8 The t Test (cont) ( 29 j H , hypothesis null accept the o whether t determine to rule rejection a with along statistic our use then will We : for statistic the" " form to need first e our test w perform To t se t t j j j Economics 20 - Prof. Anderson 9 t Test: One-Sided Alternatives Besides our null, H , we need an alternative hypothesis, H 1 , and a significance level H 1 may be one-sided, or two-sided H 1 : j > 0 and H 1 : j < 0 are one-sided H 1 : j 0 is a two-sided alternative If we want to have only a 5% probability of rejecting H if it is really true, then we say our significance level is 5% Economics 20 - Prof. Anderson 10 One-Sided Alternatives (cont) Having picked a significance level, , we...
View Full Document

Page1 / 34

multreg2 - Economics 20 - Prof. Anderson 1 Multiple...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online