Question

Determine whether the following statement is true or false. Explain your answer.

If r=0.998, then there is a positive correlation between the variables.

Choose the correct answer below.
A. The statement is true because r is closer to 1.
B. The statement is true because r is closer to 0.
C. The statement is false because r is closer to 1.
D. The statement is false because r is closer to 0.

Answer 1

The statement is true because r=0.998 suggests a strong positive correlation, as it is very close to 1. Therefore, as one variable increases, so does the other variable.

Step-by-step explanation:

The question is asking to determine the truthfulness of the statement regarding the correlation coefficient, specifically when r=0.998. To answer the question, it is important to understand that the correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1, with values close to +1 indicating a strong positive correlation, values close to -1 indicating a strong negative correlation, and values close to 0 indicating no correlation.

Given that r=0.998, it is very close to +1, which means there is a strong positive correlation between the two variables. Therefore, the correct answer to the question is:

A. The statement is true because r is closer to 1.

This answer clearly reflects that a positive value of r, especially one that is close to +1, indicates that as one variable increases, the other variable also tends to increase, thus representing a positive correlation.

To address the reference question (16.), the correlation coefficient indicates the weakest relationship when it is closest to 0 (a.).