E smaller more negative than a critical value again

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Unformatted text preview: ternatives (H0 : β1 0, H1 : β1 < 0) Reject the null hypothesis in favour of the alternative hypothesis if the estimated coe¢ cient is “too small” (i.e. smaller - more negative than a critical value). Again construct the critical value so that, if the null hypothesis is true, it is rejected in, for example, 5% of the cases. In the following example, this is the point of the t-distribution with 678 degrees of freedom that is exceeded in 5% of the cases. ! Reject if t statistic less than Lecture 4 (econometrics and simple linear regression) 1.645 EMET2007/6007 13 th March 2013 27 / 50 In this example we wish to know if the number of classes missed in a semester (missed ) explains GPA scores (termGPA): termGPAi termGPAi = β0 + β1 missedi + εi = b0 + b1 missedi + bi β β ε = 3.04 0.0043missedi + bi ε The Stata output with n = 680, has R 2 = 0.3133 and Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 28 / 50 H0 : β 1 0 H1 : β 1 < 0 One would either expect a positive e¤ect of class attendance on GPA tb = β 1 Pr (t678 < b β1 se b1 β = df = 680 0.0756 = 0.0043 17.59 2 = 678 1.645) = 0.05 and Pr (t678 < The null hypothesis is rejected since 17.59 < 2.33) = 0.01 1.645 Conclude that there is evidence that missing classes has a negative e¤ect on expected GPA Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 29 / 50 Again with p values H0 : β 1 0 H1 : β 1 < 0 One would either expect a positive e¤ect of class attendance on GPA p 0.000 = 0.000 and tb = 17.59 < 0 β1 2 1.645) = 0.05 and Pr (t678 < 2.33) = 0.01 value = Pr (t678 < The null hypothesis is rejected since 0.000 < 0.05 Conclude that there is no evidence that return on earnings has any e¤ect upon the CEO’ salary s Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 30 / 50 Testing against two-sided alternatives (H0 : β1 = 0, H1 : β1 6= 0) Reject the null hypothesis in favour of the alternative hypothesis if the absolute value of the estimated coe¢ cient is “too big” (i.e. bigger than a critical value). Again construct the critical value so that, if the null hypothesi...
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This note was uploaded on 06/15/2013 for the course EMET 2007 taught by Professor Strachan during the Two '13 term at Australian National University.

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