Question

Which of the following statements concerning Pearson r is NOT true

a. r= 0.00 represents the absence of a relationship
b. the relationship between the two variables must be nonlinear
c. r= 0.76 has the same predictive power as r= -0.76
d. r= 1.00 represents a perfect relationship
e. all the above are true

Answer 1

The incorrect statement about Pearson r is that the relationship between two variables must be nonlinear. Pearson's r is designed to measure linear relationships, and its magnitude indicates the strength of this relationship, regardless of whether the correlation is positive or negative.

Step-by-step explanation:

The statement concerning Pearson r that is NOT true is: "the relationship between the two variables must be nonlinear". Pearson's correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. Let's clarify each point related to Pearson r based on the provided options:

• r = 0.00 does indeed represent the absence of a linear relationship between two variables.
• Contrary to option b, Pearson's r is specifically for measuring the strength of a linear relationship, thus the relationship must be linear, not nonlinear.
• An r = 0.76 has the same predictive power as r = -0.76 because both coefficients have the same magnitude, indicating a strong relationship but in opposite directions.
• r = 1.00 represents a perfect positive linear relationship, while r = -1.00 would indicate a perfect negative linear relationship.

Since Pearson's r must be linear, option b is the incorrect statement and thereby not true regarding Pearson r.