Math Problem Statement

The correlation coefficient, r, is a number between:

Solution

The correct answer to this question is:

  • "-1 and 1"

The correlation coefficient, denoted by rr, measures the strength and direction of the linear relationship between two variables and always falls within the range 1r1-1 \leq r \leq 1.

  • If r=1r = 1, it indicates a perfect positive linear correlation.
  • If r=1r = -1, it indicates a perfect negative linear correlation.
  • If r=0r = 0, it suggests no linear correlation.

Would you like further details on how the correlation coefficient is interpreted?

Here are some related questions to expand your understanding:

  1. What does it mean if the correlation coefficient rr is close to 0?
  2. How is the correlation coefficient calculated between two variables?
  3. What are some limitations of using the correlation coefficient?
  4. Can a correlation coefficient alone determine causation between two variables?
  5. How does the correlation coefficient relate to covariance?

Tip: Remember that correlation only indicates the strength and direction of a linear relationship; it does not imply causation.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient
Linear Relationship

Formulas

-1 ≤ r ≤ 1

Theorems

Properties of Correlation Coefficient

Suitable Grade Level

Grades 10-12