This regression analysis examines the relationship between the number of years of formal education a person has and their annual income. According to this model, about how much more money do people who finish a 4-year college program earn each year, on average, than those with only a 2-year degree?

Dependent variable is Income
$ R $-squared $ =25.8 \% $
$ \mathrm{s}=3888 $ with 57 degrees of freedom
$ \begin{array}{lcc}\text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } \ \text { Constant } & 3984.45 & 6600 \ \text { Education } & 2668.45 & 600.1\end{array} $

A) $2710
B) $2006
C) $9321
D) $5337
E) $7968

Question

This regression analysis examines the relationship between the number of years of formal education a person has and their annual income. According to this model, about how much more money do people who finish a 4-year college program earn each year, on average, than those with only a 2-year degree?

Dependent variable is Income 
$ R $-squared $ =25.8 \% $
 $ \mathrm{s}=3888 $ with 57 degrees of freedom
$ \begin{array}{lcc}\text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } \ \text { Constant } & 3984.45 & 6600 \ \text { Education } & 2668.45 & 600.1\end{array} $

A) $2710
B) $2006
C) $9321
D) $5337
E) $7968

Quizplus · Accepted Answer

The question asks for the difference in annual income between people who finish a 4-year college program and those with only a 2-year degree. This means we need to look at the coefficient for "years of education" for both groups in the regression model. Let's assume the regression model is:

Annual Income = β0 + β1(Years of Education) + ε

where β1 is the coefficient for "years of education."

According to the question, we want to compare the difference in annual income between people with 4-year degrees and people with 2-year degrees, so we need to subtract the two coefficients. Let's say the coefficient for 4-year degrees is β4 and the coefficient for 2-year degrees is β2. Then the difference between the two is:

(β4 - β2) × (4 - 2) = β4 - β2 × 2

In other words, we are multiplying the difference in coefficients by the difference in years of education (i.e., 4 - 2 = 2) to get the difference in annual income.

Unfortunately, the regression model is not given, so we can't calculate the coefficients directly. But we can use the answer choices to estimate the difference. Based on the answer choices, the closest estimate for β4 - β2 × 2 is $5337, which is answer choice D. Therefore, the best answer is D.

This Regression Analysis Examines the Relationship Between the Number of Years