Question

The value of the coefficient of correlation ( r) a. can never be equal to the value of the coefficient of determination (r2). b. is always larger than the value of the coefficient of determination (r2). c. is always smaller than the value of the coefficient of determination (r2). d. can be equal to the value of the coefficient of determination (r2).

Answer 1

Answer:

d. can be equal to the value of the coefficient of determination (r2).

True on the special case when r =1 we have that $r^2 = 1$

Step-by-step explanation:

We need to remember that the correlation coefficient is a measure to analyze the goodness of fit for a model and is given by:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$  

The determination coefficient is given by $R= r^2$

Let's analyze one by one the possible options:

a. can never be equal to the value of the coefficient of determination (r2).

False if r = 1 then $r^2 = 1$

b. is always larger than the value of the coefficient of determination (r2).

False not always if r= 1 we have that $r^2 =1$ and we don't satisfy the condition

c. is always smaller than the value of the coefficient of determination (r2).

False again if r =1 then we have $r^2 = 1$ and we don't satisfy the condition

d. can be equal to the value of the coefficient of determination (r2).

True on the special case when r =1 we have that $r^2 = 1$