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) as hereunder. A total number of _(i) employees were selected for this study:

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

Moreover, by applying this model on a database, the researcher found that the GRETL results shows the "coefficient of determination"= 0.130537 (under 5% level of significance)

Using the above findings, answer the following questions:

A-Comment about the "coefficient of determination" on this model.

B-What is the other name of the coefficient of determination?

C-By looking at this coefficient, what can be concluded about the goodness of fit for the model?

Answer 1

Answer a: We know that Coefficient of determination is defined as the amount of variation in the dependent variable that can be explained by the model. Now here in the regression results it has been given that the coefficient of determination is 0.1305 which simply means that approximately 13.05 percent of the variation in the salary of the selected employees can be explained by the model.

Answer b: The other name for the coefficient of determination is R square.

Answer c: Since the coefficient of determination value is very low i.e. only around 13 percent, it means that the regression model is not a good fit. Usually an R square with a value of above eighty percent is considered to be a good fit of the regression model. In general, higher is the value of the r square better fit is the regression model. So we can say that the regression model can't explain the variation in the salaries of the selected employees of an organization.