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estimated coe¢ cient is “too large” (i.e. larger than a critical value).
Construct the critical value so that, if the null hypothesis is true, it is
rejected in, for example, 5% of the cases.
In the given example, this is the point of the t-distribution with 207
degrees of freedom that is exceeded in 5% of the cases. ! Reject if t statistic greater than 1.66 Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 17 / 50 Reject if t-statistic
greater than 1.66 1.66 ecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 18 / 50 Recall the CEO example: true and estimated models:
salaryi = β0 + β1 salesi + εi
= b0 + b1 salesi + bi
= 1174 + 0.0155salesi + bi
ε The Stata output with n = 209, has R 2 = 0.0096 and Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 19 / 50 0 H1 : β 1 > 0 H0 : β 1 One would expect a positive e¤ect of sales on CEO salary tb =
β1 se b1
β = df = 209 Pr (t207 > 1.66) 0.0155
2 = 207 0.05 and Pr (t207 > 2.6) = 0.01 The null hypothesis is rejected since 1.74 > 1.66
Conclude that there is evidence that company sales has an e¤ect
upon the CEO’ salary
Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 20 / 50 Computing p values for t-tests If the signi…cance level is made smaller and smaller, there will be a
point where the null hypothesis cannot be rejected anymore
The reason is that, by lowering the signi…cance level, one wants to
avoid more and more to make the error of rejecting a correct H0
The smallest signi…cance level at which the null hypothesis is still
rejected, is called the p value of the hypothesis test
A small p value is evidence against the null hypothesis because one
would reject the null hypothesis even at small signi…cance levels
A large p
p value is evidence in favor of the null hypothesis values are more informative than tests at …xed signi…cance levels Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 21 / 50 How the p-value is computed (here: two-sided test) The p-value is the signi...
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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.
- Two '13