A study of class attendance and grades among first-year students at a state university showed that, in general, students who missed a higher percent of their classes earned lower grades. Class attendance explained 16% of the variation in grade index among the students. What is the numerical value of the correlation between percent of classes attended and grade index

the numerical value of the correlation between percent of classes attended and grade index is r = 0.4

Step-by-step explanation:

Given the data in the question;

we know that;

the coefficient of determination is r²

while the correlation coefficient is defined as r = √(r²)

The coefficient of determination tells us the percentage of the variation in y by the corresponding variation in x.

Now, given that class attendance explained 16% of the variation in grade index among the students.

so

coefficient of determination is r² = 16%

The correlation coefficient between percent of classes attended and grade index will be;

r = √(r²)

r = √( 16% )

r = √( 0.16 )

r = 0.4  

Therefore,  the numerical value of the correlation between percent of classes attended and grade index is r = 0.4