Question

If the value of the coefficient of determination of 0.64, what is the value of the coefficient of correlation?
a). 0.4
b). 0.8
c). 0.08
d). 0.04

Answer 1

Hint: To find the value of the coefficient of correlation we will first define the coefficient of correlation and coefficient of determination and then by using the relationship among coefficient of correlation and coefficient and coefficient of determination. When we square the coefficient of correlation, we get the coefficient of determination. For example: The coefficient of determination is 0.64 or 64% and the coefficient of determination is symbolized by r-squared , where r is the coefficient of correlation. Hence, a coefficient of determination of 0.36 or 36% means that the coefficient of correlation was 0.6 or 60%.

Complete step by step answer:
Before finding the coefficient of correlation let us first define the coefficient of determination. We can define coefficient of determination as a statistic which represents the association between independent and dependent variables. Coefficient of determination is defined as the percentage change in the amount of dependent variable that is “explained by” the change in the independent variable.
And, the relation between coefficient of correlation and coefficient of determination is that when coefficient of correlation is squared it becomes the coefficient of determination.
In simpler words we can say that: \[\left( \text{coefficient of determination} \right)\text{ }=~~{{\left( \text{coefficient of correlation} \right)}^{2}}..........(1)\]
From the question we can see that the coefficient of determination is 0.64.
So, after putting the value of coefficient of determination in equation (1), we will get:
$\left( 0.64 \right)={{(\text{coefficient of correlation})}^{^{2}}}$
 \[\Rightarrow (\text{coefficient of correlation})=\sqrt{0.64}\]
So, coefficient of correlation = 0.8.

So, the correct answer is “Option B”.

Note: Students are required to memorize the relation among the coefficient of determination and the coefficient of correlation. And they should not be confused among the coefficient of determination and coefficient of correlation in the formula that is to be squared.