For the 2012 GSS, the regression of respondent's income in constant dollars (Y) on years of education (X) yields the following equation: Y = -45,204.31 + 5,293.56X.
A) What is the value of the regression coefficient?
B) How much does income (Y) increase for each increase of one year of education?
C) What is the predicted income in 2012 for a person with a bachelor's degree (16 years of education)?
D) The correlation between income and years of education is .28. What does this tell you about this relationship?

Question

Quizplus · Accepted Answer

The regression coefficient in this context refers to the slope of the regression line, which represents the average change in the dependent variable (Y, respondent's income in constant dollars) for each one-unit change in the independent variable (X, years of education). In the given regression equation Y = -45,204.31 + 5,293.56X, the regression coefficient is 5,293.56.
b. How much does income (Y) increase for each increase of one year of education?
For each additional year of education, the income (Y) increases by the regression coefficient, which is $5,293.56.
c. What is the predicted income in 2012 for a person with a bachelor's degree (16 years of education)?
To predict the income for a person with a bachelor's degree, which typically represents 16 years of education, we substitute X with 16 in the regression equation:
Y = -45,204.31 + 5,293.56(16)
Y = -45,204.31 + 84,696.96
Y = 39,492.65
The predicted income in 2012 for a person with a bachelor's degree is $39,492.65.
d. The correlation between income and years of education is .28. What does this tell you about this relationship?
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient of .28 indicates a positive but weak linear relationship between income and years of education. This means that as years of education increase, income tends to increase as well, but the relationship is not very strong. A correlation of .28 suggests that other factors besides education likely have a significant impact on income, and that years of education alone do not explain most of the variability in income.

For the 2012 GSS, the Regression of Respondent's Income in Constant