a) Do there appear to be important regional differences? Use an appropriate hypothesis test to explain your answer.b) Explain why the regressor West is omitted from the regression?c) Juanita is a 28-year-old female college graduate from the South. Molly is a 28-year-old female college graduate from the West. Jennifer is a 28-year-old female college graduate from the Midwest.(i) Construct a 95% confidence interval for the difference in expected earningsbetween Juanita and Molly.(ii) Explain how you would construct a 95% confidence interval for the difference in expected earnings between Juanita and Jennifer. (Hint: What would happen if you included West and excluded Midwest from the regression?) Question 5The data set (2012 Current Population Survey, U.S.) used for this question consists ofinformation on 7440 observations of full-time, full-year workers. The highest educationalachievement for each worker was either a high school diploma or a bachelor's degree.The workers' ages ranged from 25 to 34 years. The data set also contains informationon the region of the country where the person lived.The following variables are included in the data set:AHE= average hourly earnings (in 2012 US dollars, S)= binary variable (1 if college. O high school)= binary variable (1 if female, O if male)= age (in years)CollegeFemaleAgeNortheast - binary variable (1 Region = Northeast, 0 otherwise)Midwest= binary variable (1 if Region = Midwest, 0 otherwise)= binary variable (1 i Region = South, 0 otherwise)= binary variable (1 i Region = West, O otherwise)SouthWestThe following regression results are obtained based on the above data set:RegressorCollege (X,)Dependent variable: average hourly earnings (AHE)(1)8.31(2)(3)8.328.34 The following regression results are obtained based on the above data set:Dependent variable: average hourly earnings (AHE)RegressorCollege (X,)(1)(2)(3)8.31(0.23)8.34(0.22)8.32(0.22)Female (X,)-3.85-3.81(0.22)0.51(0.04)-3.80(0.23)(0.22)Age (X,)0.51(0.04)Northeast (X,)0.18(0.36)Midwest (X,)-1.23(0.31)South (X,)-0.43(0.30)2.05Constant17.021.87(0.17)(1.18)(1.18)Summary Statistics and Joint TestsF-statistic for regional effect = 0Standard error of regression7.389.799.689.670.1620.1800.182N744074407440Note: Standard errors in parentheses.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a) Do there appear to be important regional differences? Use an appropriate hypothesis test to explain your answer.
b) Explain why the regressor West is omitted from the regression?
c) Juanita is a 28-year-old female college graduate from the South. Molly is a 28-year-old female college graduate from the West. Jennifer is a 28-year-old female college graduate from the Midwest.
(i) Construct a 95% confidence interval for the difference in expected earnings
between Juanita and Molly.
(ii) Explain how you would construct a 95% confidence interval for the difference in expected earnings between Juanita and Jennifer. (Hint: What would happen if you included West and excluded Midwest from the regression?)

The following regression results are obtained based on the above data set:
Dependent variable: average hourly earnings (AHE)
Regressor
College (X,)
(1)
(2)
(3)
8.31
(0.23)
8.34
(0.22)
8.32
(0.22)
Female (X,)
-3.85
-3.81
(0.22)
0.51
(0.04)
-3.80
(0.23)
(0.22)
Age (X,)
0.51
(0.04)
Northeast (X,)
0.18
(0.36)
Midwest (X,)
-1.23
(0.31)
South (X,)
-0.43
(0.30)
2.05
Constant
17.02
1.87
(0.17)
(1.18)
(1.18)
Summary Statistics and Joint Tests
F-statistic for regional effect = 0
Standard error of regression
7.38
9.79
9.68
9.67
0.162
0.180
0.182
N
7440
7440
7440
Note: Standard errors in parentheses.

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