Answer: Option C
[tex]r ^ 2 = 0.684[/tex]
Step-by-step explanation:
The correlation coefficient r is a measure of how strong the relationship between two variables x and y is.
If the value of r is positive then the correlation is positive and that implies that the variable x grows together with the variable y.
If the value of r is negative that means that the correlation is negative and that implies that when the variable x grows then the variable y decreases.
Then for a relationship, the coefficient of determination [tex]r ^ 2[/tex] is a measure of how well the model fit the data or how accurate the model is. While r is closer to 1, better is the precision of the model.
The coefficient of determination [tex]r ^ 2[/tex] for a linear relationship is calculated as the square of the correlation coefficient.
In this problem we have that the correlation coefficient r is
[tex]r = 0.827[/tex]
then the coefficient of determination is:
[tex]r ^ 2 = 0.827 ^ 2[/tex]
[tex]r ^ 2 = 0.684[/tex]
The answer is option C
