EMET2007 Lecture 4

These would be the critical values for a 5

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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 two-sided case, the p-value is thus the probability that the t-distributed 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 p-value 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 one-sided al...
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