1 2 3 1 2 3 t and F conflicts Say all three t tests fail to reject the null And

# 1 2 3 1 2 3 t and f conflicts say all three t tests

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1 = 0 ; ? 2 = 0 ; ? 3 = 0 ? 1 = 0 ; ? 0 : ? 2 = 0 ; ? 0 : ? 3 = 0
t and F conflicts Say all three t tests “fail to reject” the null. And the F-test strongly rejects the null What is your conclusion on this model? 60 ? 0 : ? 1 = 0 ; ? 0 : ? 2 = 0 ; ? 0 : ? 3 = ? 0 : ? 1 = 0 ; ? 2 = 0 ; ? 3 = 0 Could be multicollinearity where the individual standard errors are high but the overall model works well.
t and F conflicts Example 2: Say all one of the three t tests strongly rejects the null. And the F-test fails to reject the null What is your conclusion on this model? 61 Most likely the other two variables are “junk” with zero coefficients.
t and F conflicts The fact that these two perfectly valid tests lead to different answers is one of the oddities of classical statistics and emphasizes the value of treating tests as measures of the strength of the evidence rather than taking literally the determination to reject or fail to reject. 62
In Stata Model Hypothesis Command to regress regress y x1-x5 testparm x3 x4 x5 /*does the F-test*/ 63 ? 0 : ? 3 = ? 4 = ? 5 = 0
In Stata Model Hypothesis Command to regress regress y x1-x5 testparm x3 x4 x5 , equal /*does the F-test*/ 64 ? 0 : ? 3 = ? 4 = ? 5
In Stata Model Hypothesis Command to regress regress y x1-x5 test x3==1, accumulate test x4==0, accumulate test x5==2 65 ? 0 : ? 3 = 1 ; ? 4 = 0 ; ? 5 = 2
Other methods to test “joint” hypothesis Model Test: Rewrite by adding and subtracting Test is now: 66 ? 0 : ? 2 = ? 3 ? 2 ? 3 ? ( ¿¿ 3 ? 2 ) ? 3 + ? ? = ? 0 + ? 1 ? 1 + ? 2 ( ? 2 + ? 3 ) + ¿ ? = ? 0 + ? 1 ? 1 + ? 2 ( ? 2 + ? 3 ) + ? 3 ? 3 + ? 0 : ? 3 = 0
Multiple Regression Analysis with Qualitative Information Interactions between dummy variables and continuous variables. Recall Allows different intercepts for different groups but not different slopes. But with an interaction 67 ???? = ? 0 + ? 0 ?????? + ? 1 ???? + ? 1 ( ?????? ???? ) + ?
Multiple Regression Analysis with Qualitative Information Interactions involving dummy variables Allowing for different slopes the E(earnings|female, educ) are: Interesting hypotheses = intercept men = intercept women = slope men = slope women Interaction term The return to education is the same for men and women The whole wage equation is the same for men and women 68
Multiple Regression Analysis with Qualitative Information Interacting both the intercept and the slope with the female dummy enables one to model completely independent wage equations for men and women 69 ???? = ? 0 + ? 0 ?????? + ? 1 ???? + ? 1 ( ?????? ???? ) + ? ? 0 ¿ 0 ? 1 ¿ 0 ? 0 ¿ 0 ? 1 ¿ 0
Multiple Regression Analysis with Qualitative Information Testing for differences in regression functions across groups. Let’s discuss 2 ways to do this. 1 st way – Estimate a fully interacted model and test the null that all coefficients on all interactions are zero. Say we are modeling earnings based on education and sex. Test is 70 ???? = ? 0 + ? 1 ???? + ? 2 ( ???? ??? )+ ? 3 ??? + ? 4 ( ??? ??? )+ ? ? 0 : ? 2 = ? 4 = 0
Multiple Regression Analysis with Qualitative Information 2 nd way – Estimate the model pooling the 2 groups and then separately for men and women (3 models). Record the SSR (sum of squared residuals) in each case and construct an F-statistic 71 SSR p – SSR from pooled model (restricted) SSR 1 – SSR from only group 1 SSR 2 – SSR from only group 2 K+1 – the number of restrictions implicit in the pooling n-(2k+1) is the number of degrees of freedom in the unrestricted model
Multiple Regression Analysis with Qualitative Information

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