Α 005 reject the ho if the f test statistic is 311

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α = 0.05 Reject the Ho if the F-test statistic is > 3.11 and p-value < 0.05. EXCEL command for critical value: =F.INV.RT(0.05,2,81) Step #3 F = ( .6653 .6319 )/ 2 ( 1 .6653 )/ 81 = 4.04 p-value = 0.021 Note: The p-value was found in EXCEL using the command: =F.DIST.RT(4.04,2,81) Step #4 Since 4.04> 3.11 AND 0.021< 0.05 Reject Ho; there is some general kind of functional form misspecification. #2. You will using the data infmrt.dta for this question, this is similar to the dataset used in C4 [p. 339]. (a) Consider the regression equation on p. 331 [9.44]. Use a Davidson-MacKinnon approach to test which of two possible specifications might be “better:” the version using natural lns for the X-variables such as estimated in [9.44] OR the specification infmort = β 0 + β 1 pcinc + β 2 physic + β 4 popul + u , i.e. a version of the regression in which the X-regressors are used as levels. Be sure to use the discussion on p. 308 in your work. 2
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IMPORTANT to fully explore this Davidson-MacKinnon approach you should have two different “four- step” t-tests AND a discussion of how to interpret the results of these tests. t-test Step #1 H 0 A : θ B = 0 H a A : θ B 0 Step #2 This hypothesis test is based on the t-distribution with 97 degrees of freedom. α = 0.05 Reject the Ho if the t-test statistic is ≥ 1.985 or ≤ -1.985 and p-value < 0.05. Note the critical values were found in EXCEL using the command: =T.INV.2T(.05,97) Step #3 t = 3.57 .536 =− 6.66 p-value = 0.000 Step #4 Since –6.66 < –1.985 AND 0.000 < 0.05 Reject Ho. t-test Step #1 H 0 B : θ A = 0 H a B : θ A 0 3
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Step #2 This hypothesis test is based on the t-distribution with 97 degrees of freedom. α = 0.05 Reject the Ho if the t-test statistic is ≥ 1.985 or ≤ -1.985 and p-value < 0.05. Note the critical values were found in EXCEL using the command: =T.INV.2T(.05,97) Step #3 t = 3.634 . 378 = 9.61 p-value = 0.000 Step #4 Since 9.61 > 1.985 AND 0.000 < 0.05 Reject Ho. Based on the results we are rejecting both models; so there is no model that is better than another according to the test. Based on this we need to take a closer look at what the regressions are telling us, measuring a 1 unit increase in the doctors per 100k civilian population is not very useful, so it is likely more preferable to have that variable in a log form to estimate a percentage increase ceteris paribus effect on deaths per 1000 live births. The coefficient is a little bit more of what you also expect. So my suggest would be to use the level-log model.
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