Unformatted text preview: ficance level at which one is
indifferent between rejecting and not rejecting the
null hypothesis.
These would be the
critical values for a 5%
significance level In the twosided case, the pvalue is thus the
probability that the tdistributed variable takes on
a larger absolute value than the realized value of
the test statistic, e.g.: From this, it is clear that a null hypothesis is
rejected if and only if the corresponding pvalue is
smaller than the significance level.
value of test statistic For example, for a significance level of 5% the tstatistic would not lie in the rejection region. Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 22 / 50 Test again with p values
H0 : β 1 0 H1 : β 1 > 0 One would expect a positive e¤ect of sales on CEO salary p 0.084
= 0.042 and tb = 1.74 > 0
β1
2
> 1.66) = 0.05 and Pr (t207 > 2.6) = 0.01 value = Pr (t207 The null hypothesis is rejected since 0.042 < 0.05
Conclude that there is evidence that company sales has an e¤ect
upon the CEO’ salary
s Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 23 / 50 Recall the other CEO example: true and estimated models:
salaryi
salaryi = β0 + β1 roei + εi
= b0 + b1 roei + bi
β
β
ε
= 963.19 + 18.50roei + bi
ε The Stata output with n = 209, has R 2 = 0.0132 (a bit higher) and Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 24 / 50 0 H1 : β 1 > 0 H0 : β 1 One would expect a positive e¤ect of ROE on CEO salary
tb =
β b
β1 1 β
se b1 df = 209 Pr (t207 > 1.66) = 18.50
= 1.66
11.12
2 = 207 0.05 and Pr (t207 > 2.6) = 0.01 The null hypothesis is neither rejected nor ‘ rejected’since
not
1.66 = 1.66
Cannot make a conclusion about the e¤ect of 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 25 / 50 Again with p values
H0 : β 1 0 H1 : β 1 > 0 One would expect a positive e¤ect of ROE on CEO salary
p 0.098
= 0.049 and tb = 1.66 > 0
β1
2
> 1.66) = 0.05 and Pr (t207 > 2.6) = 0.01 value = Pr (t207 The null hypothesis is (just) rejected since 0.049 < 0.05
Conclude that there is (weak) 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 26 / 50 Testing against onesided al...
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 Two '13
 strachan
 Normal Distribution, Regression Analysis, Statistical hypothesis testing, Tn

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