Question

A researcher has designed the relationship between the salaries of selected employees of an organization (shown as "EARN" in $/hour) and their years of education (shown as "YRSEDUC", in years) and their age (shown as "AGE" in years) as hereunder. A total number of _(i) employees were selected for this study:

EARN_(i) = B₍₀₎ + B₍₁₎ YRSEDUC_(i) + B₍₂₎ AGE_(i)  + u_(i)

Using the above findings, answer the following questions:

A-Comment about the slope coefficient of the variable "AGE"

B-What do you expect to happen on the coefficient of determination of this regression as opposed to the same on a regression with only explanatory variable "AGE"? Explain your reasons.

Answer 1

Answer a: The slope coefficient of the variable age is B2 which basically shows that as the of an employee increases by one year, the salary of the same employee on an average increases by B2 $/hour holding his years of education as constant.

Answer b: We know that coefficient of determination is defined as the amount of variation in the dependent variable that can be explained by the regression model. Usually it happens that we the inclusion of more and more explanatory variables, the coefficient of determination rises.

Now suppose if we don't include the years of education as the independent or the explanatory variable in the regression model the coefficient of determination is going to fall down. Years of education being one of the most important factors in determining the salary of the employee will lead to a rise in the overall variation of the model and also help in getting rid of the problem of omitted variable bias. Also, with the inclusion of just variable age in the model, the coefficient of determination will decrease which will also have an impact on the regression results. Moreover if we don't include years of education in the model, then it becomes the part of the random error term as a result of which we can get inaccurate estimates and also lower value of R square.

Higher is the value of R square, better fit is the regression model. So an exclusion of years of education there will be a fall in the explained sum of squares, thus leading to a fall in the coefficient of determination.