Question

A college professor investigated the relationship between the number of absences and the final grade for the course. He found that more absences were associated with lower final grades. Number of absences explained 25% of the variation is final grades. The correlation coefficient for this relationship will be ______.

Answer 1

-0.5

Explanation:

The proportion of the variance in the dependent variable (final grade) that is predictable from the independent variable (number of absences) is called the coefficient of determination (R² = 0.25).

The correlation coefficient (R) is the square root of coefficient of determination:

`R =√(0.25)\\ R = \pm 0.5`

Since the higher the number of absences, the lower the grade, there is a downhill relationship between the variables and the correlation coefficient must be negative. Therefore, R = -0.5