Question

It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. The Excel output from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big Ten university gives R Square = 0.5774 The interpretation of the coefficient of determination in this regression is that

Answer 1

Options :

B) ACT scores account for 57.74% of the total fluctuation in GPA.

B) ACT scores account for 57.74% of the total fluctuation in GPA.

C) GPA accounts for 57.74% of the variability of ACT scores.

D) None of the above.

Answer:

B) ACT scores account for 57.74% of the total fluctuation in GPA.

Explanation:

The R-squared value, called the Coefficient of determination gives the percentage or proportion of variation in the dependent variable which is due to or caused by the independent variable.

In the study above, the independent variable is the ACT score, is used to draw a regression relationship between the GPA of students, with GPA being the dependent variable.

The R² :value being 0.5774 means that (0.5774 * 100%) = 57. 74 % of variation in students GPA is caused by the regression line (independent variable which is the ACT SCORE).

HENCE, we can conclude that ACT Score is responsible of 57. 74 % variation in GPA while the remaining percentage is due to other factors.