If the r-value or correlation coefficient of a data set is 0.827, what is the coefficient of determination to three decimal places?

a. 0.884
b. 0.627
c. 0.684
d. 0.827

Option C  

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 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 for a linear relationship is calculated as the square of the correlation coefficient.

In this problem we have that the correlation coefficient r is

then the coefficient of determination is:

The answer is option C

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