S.3. From the data given in Table 2.6 on earnings and education, we obtained the
ID: 1110582 • Letter: S
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S.3. From the data given in Table 2.6 on earnings and education, we obtained the following regression [see Eq. (3.7.3) Meanwagn= 0.7437 + 0.6416 Education se-(0.8355) I-( ) (9,6536) r2-0.8944 "-13 a. Fill in the missing numbers. b. How do you interpre·the coefficient 064167 e. Would you reject the hypothesis that education has no effect whatso ever on wages? Which test do you use? And why? What is the p value of your test statistic? the slope coefficient is zcro. Which test do you use and why? you. Could you have obiained it from the other information given in d. Set up the ANOVA table for this esample and test the hypothesis that e. Suppose in the regression given above the value was not given to the regression? a. , )-0.64 16/ 9.6536-0.0665· t(.) " 0.7437 / 0.8355-0.5901 b. The coefficient 0.6416 of education suggests that for every one-year of schooling results in 6416% increase, on average, in the meanwage. This coefficient highly significant, implying that there is a significant relationship between meanwage and education, This is because the observed t-statistic of 9.6536 of the coefficient is much higher than its critical value of 2.201 for 1 degree of freedom at the 5% significance level. c. The t-statistic can be used to test the null hypothesis that education has no effect on meanwage. As shown in b, the t-statistic of the coefficient is much higher than its critical value at the 5% significance level. This is done as follows: H0: 2-0 06416-0-9,6539 0.06646 seif ·2201 4m . 9.6539 > 2.201 Ho is rejected strongly at the 5 significance level. At this value of t-statistic, thus the probability value is practically zero. ESS : d RSS -In the case of the two-variable regression model, the F-statistic is equal to t- 9.6536 2-91.46 e. The value R2 can be calculated by using information about TSS and ESSExplanation / Answer
e) Given the t- value we can calculate the F-statistic.
Using the Formula F = (R2/1-R2)*(n-k/k-1), We can calculate the R2 value.
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