Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using 2012 Data from the Current Population Survey Dependent variable: average hourly earnings (AHE). Regressor College (X₂) Female (X₂) Age (X₁) Northeast (X₁) Midwest (X₂) South (X) Intercept Summary Statistics and Joint Tests F-statistic for regional effects=0 SER R² A 8.31 (0.23) <-3.85 (0.23) 17.02 (0.17) 9.79 0.162 7440 (2) 8.32 (0.22) -3.81 (0.22) 0.51 (0.04) 1.87 (1.18) 9.68 0.180 7440 (3) 8.34 (0.22) -3.80 (022) 0.52 (0.04) 0.18 (0.36) -1.23 (0.31) i. Individual significance of X4, X5, and X6 : A. Specify the null and alternative hypotheses. -0.43 (0.30) 2.05 (1.18) 7.38 9.67 0.182 7440 (a) Test the individual significance of College and Female at the significance level of 5% in all three regressions. (b) Note that there can be other variables that influence AHE but are not in- cluded in the regressions. This possibility of omitting variables can cause bias in the coefficients of College and Female. Assess the following state- ment: "in all of the regression, the coefficient on Female is negative, large, and statistically significant. This provides strong statistical evidence of gender discrimination in the US labor market." Present statistical argu- ments for your evaluation. (c) Discuss how to modify the regressions to allow for the effect of college education to differ by gender in Regression (1). (d) Find the intercept and the slope of College for males who live in Midwest in Regression (3). (e) Find the intercept and the slope of College for females who live in Midwest in Regression (3). (f) Does Regression (3) allow the regional effects differ by gender? (In other words, does Regression (3) allow the gender gap to vary with region?) (g) Test both individual and joint significance of regional dummies at the 5% significance level.
Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using 2012 Data from the Current Population Survey Dependent variable: average hourly earnings (AHE). Regressor College (X₂) Female (X₂) Age (X₁) Northeast (X₁) Midwest (X₂) South (X) Intercept Summary Statistics and Joint Tests F-statistic for regional effects=0 SER R² A 8.31 (0.23) <-3.85 (0.23) 17.02 (0.17) 9.79 0.162 7440 (2) 8.32 (0.22) -3.81 (0.22) 0.51 (0.04) 1.87 (1.18) 9.68 0.180 7440 (3) 8.34 (0.22) -3.80 (022) 0.52 (0.04) 0.18 (0.36) -1.23 (0.31) i. Individual significance of X4, X5, and X6 : A. Specify the null and alternative hypotheses. -0.43 (0.30) 2.05 (1.18) 7.38 9.67 0.182 7440 (a) Test the individual significance of College and Female at the significance level of 5% in all three regressions. (b) Note that there can be other variables that influence AHE but are not in- cluded in the regressions. This possibility of omitting variables can cause bias in the coefficients of College and Female. Assess the following state- ment: "in all of the regression, the coefficient on Female is negative, large, and statistically significant. This provides strong statistical evidence of gender discrimination in the US labor market." Present statistical argu- ments for your evaluation. (c) Discuss how to modify the regressions to allow for the effect of college education to differ by gender in Regression (1). (d) Find the intercept and the slope of College for males who live in Midwest in Regression (3). (e) Find the intercept and the slope of College for females who live in Midwest in Regression (3). (f) Does Regression (3) allow the regional effects differ by gender? (In other words, does Regression (3) allow the gender gap to vary with region?) (g) Test both individual and joint significance of regional dummies at the 5% significance level.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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Please help me with question d, e, f, g, h, and I. Thank you.
Transcribed Image Text:Results of Regressions of Average Hourly Earnings on Gender and Education Binary
Variables and Other Characteristics Using 2012 Data from the Current Population Survey
Dependent variable: average hourly earnings (AHE).
Regressor
College (X₂)
Female (X₂)
Age (X₁)
Northeast (X₂)
Midwest (X₂)
South (X)
Intercept
Summary Statistics and Joint Tests
F-statistic for regional effects=0
SER
R²
R
8.31
(0.23)
-3.85
(0.23)
17.02
(0.17)
9.79
0.162
7440
(2)
8.32
(0.22)
-3.81
(0.22)
0.51
(0.04)
1.87
(1.18)
9.68
0.180
7440
(3)
8.34
(0.22)
-3.80
(0.22)
0.52
(0.04)
0.18
(0.36)
-1.23
(0.31)
i. Individual significance of X4, X5, and X₁:
A. Specify the null and alternative hypotheses.
B. Calculate the T-statistics for the three dummies.
-0.43
(0.30)
2.05
(1.18)
7.38
9.67
0.182
7440
(a) Test the individual significance of College and Female at the significance
level of 5% in all three regressions.
(b) Note that there can be other variables that influence AHE but are not in-
cluded in the regressions. This possibility of omitting variables can cause
bias in the coefficients of College and Female. Assess the following state-
ment: "in all of the regression, the coefficient on Female is negative, large,
and statistically significant. This provides strong statistical evidence of
gender discrimination in the US labor market." Present statistical argu-
ments for your evaluation.
(c) Discuss how to modify the regressions to allow for the effect of college
education to differ by gender in Regression (1).
(d) Find the intercept and the slope of College for males who live in Midwest
in Regression (3).
(e) Find the intercept and the slope of College for females who live in Midwest
in Regression (3).
(f) Does Regression (3) allow the regional effects differ by gender? (In other
words, does Regression (3) allow the gender gap to vary with region?)
(g) Test both individual and joint significance of regional dummies at the 5%
significance level.
Transcribed Image Text:C. Specify the critical values you refer to. Use the statistical table
provided in class.
D. Conclude regarding the individual significance.
ii. Joint significance of X4, X5, and X₁ :
A. Specify the null and alternative hypotheses.
B. Which regression is restricted and unrestricted models?
C. Calculate the F-statistic by specifying the formula you use.
Be specific with degrees of freedom.
D. Specify the critical values you refer to. Use the statistical table
provided in class.
E. Conclude regarding the joint significance
(h) Which regression (among (1), (2), and (3)) do you believe is the best model
and why? Clearly present the relevant statistics you refer to to reach the
conclusion.
(i) Suppose you believe regression (3) is the best model and decide to use (3)
to estimate the impact of college education on Average Hourly Earnings.
As you observe the bias seems to be corrected in (3), compared with (1)
and (2), you state that "the true population coefficient of College is 8.34."
Is this statement is True or False? Why?
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