expecteU UllILIU 7.4 Using the regression results in column (3): a. Do there app
ID: 3336514 • Letter: E
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expecteU UllILIU 7.4 Using the regression results in column (3): a. Do there appear to be important regional differences? Use an app priate hypothesis test to explain your answer. Results of Regressions of Average Hourly Earnings on Gender and Education Binary | Variables and Other Characteristics Using 2012 Data from the Current Population Survey (2) (3) Dependent variable: average hourly earnings (AHE. (1) Regressor 8.31 College (X) (0.23) Female (X) 3.85 (0.23) Age (X3 8.32 (0.22) 8.34 (0.22) -3.80 -3.81 (0.22) (0.22) 0.51 0.52 (.04) (0.04) Northeast (x4) 0.18 (036) Midwest (X5) South (X ) 1.23 (031) -0.43 (.30) 2.05 (118) Intercept 17.02 (017) 1.87 (1.18) Summary statistics and Joint Tests F-statistic for regional effects = 0 SER 1.38 9.79 9.68 9.67 0.162 0.180 0.182 7440 7440 7440Explanation / Answer
In the above regression problem three regions have been considered viz. Northeast, Midwest and South.
We can do one thing here. In the third column, it appears that the regression equation consists of the 3 regions and also the R2 value for the 3rd regression is the highest (0.182) so if we test the significance of the regression coefficients of the 3 regions and if any one of them gets rejected we can say that there is obviously a regional effect and hence there might be a regional difference.
We can conduct the test by,
H01 : There is no regional effect of Northeast or regression coefficient of the variable X4 is insignificant
against H11 : There is a regional effect due to Northeast or regression coefficient of the variable X4 is significant
H012 : There is no regional effect of Midwest or regression coefficient of the variable X5 is insignificant
against H12 : There is a regional effect due to Midwest or regression coefficient of the variable X5 is significant
H01 : There is no regional effect of South or regression coefficient of the variable X6 is insignificant
against H11 : There is a regional effect due to South or regression coefficient of the variable X6 is significant
Here we can draw our conclusions based on the p-values of the tests which are already given in the bracket under every coefficient value.
For the three regions it seems that the p-value is greater than 0.05 and hence we can accept all the null hypotheses at 5% level of significance and conclude on the basis of the given data that the regional effects are insignificant and as a result there is not any regional difference.
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