Analysis of Multiple Regression
Introduction
Team D will examine positive relationship of wages with multiple variables. The question is, are wages dependent on the gender, occupation, industry, years of education, race, years of work experience, marital status, and union membership. We will use the technique of linear regression and correlation. Regression analysis in this case should predict the value of the dependent variable (annual wages), using independent variables (gender, occupation, industry, years of education, race, and years of work experience, marital status, and union membership).
Regression Analysis
Based on our initial findings from MegaStat, we built the following model for regression (coefficient factors are rounded to the nearest hundredth):
Wages (Y) = -12,212.98 + 167.51(Industry) + 71.13(Occupation) + 3,085.27(Years of Education) – 6,172.13(Non-White) + 1,857.06(Hispanic) – 11,822.96(Gender) + 356.27(Years of Experience) + 4,589.46(Marital Status) – 4,018.87(Union Member)
Global Test:
Ho: All regression coefficients for the variables in the population are zero
H1: Not all regression coefficients are zero
Significance level = 0.05
Decision rule: Reject Ho if p-value < 0.05
The p-value generated by the regression analysis is non-zero (4.42x10-7), therefore we reject Ho and conclude that regression is a good fit for this model.
Individual tests: Ho: Regression coefficient for each variable is zero
H1: Regression coefficient for each variable is not zero
Significance level = 0.05
Decision rule: Reject Ho if p-value < 0.05
Because these are all t-tests, we can read the p-values of these tests from the Regression output. he variables with p-values less than 0.05 have significant impact on wages earned, also that variables with p-values greater than 0.05 do not have significant impact on wages. According to the MegaStat output, the variables that significantly affect wages are education (p = 2.17x10-6), gender (p = .0001), and experience (p = .0083).
Team D will examine positive relationship of wages with multiple variables. The question is, are wages dependent on the gender, occupation, industry, years of education, race, years of work experience, marital status, and union membership. We will use the technique of linear regression and correlation. Regression analysis in this case should predict the value of the dependent variable (annual wages), using independent variables (gender, occupation, industry, years of education, race, and years of work experience, marital status, and union membership).
Regression Analysis
Based on our initial findings from MegaStat, we built the following model for regression (coefficient factors are rounded to the nearest hundredth):
Wages (Y) = -12,212.98 + 167.51(Industry) + 71.13(Occupation) + 3,085.27(Years of Education) – 6,172.13(Non-White) + 1,857.06(Hispanic) – 11,822.96(Gender) + 356.27(Years of Experience) + 4,589.46(Marital Status) – 4,018.87(Union Member)
Global Test:
Ho: All regression coefficients for the variables in the population are zero
H1: Not all regression coefficients are zero
Significance level = 0.05
Decision rule: Reject Ho if p-value < 0.05
The p-value generated by the regression analysis is non-zero (4.42x10-7), therefore we reject Ho and conclude that regression is a good fit for this model.
Individual tests: Ho: Regression coefficient for each variable is zero
H1: Regression coefficient for each variable is not zero
Significance level = 0.05
Decision rule: Reject Ho if p-value < 0.05
Because these are all t-tests, we can read the p-values of these tests from the Regression output. he variables with p-values less than 0.05 have significant impact on wages earned, also that variables with p-values greater than 0.05 do not have significant impact on wages. According to the MegaStat output, the variables that significantly affect wages are education (p = 2.17x10-6), gender (p = .0001), and experience (p = .0083).