Math Problem Statement

you are a scientist who wishes to obtain as high a correlation as possible. Which one of the following would you consider to be the best result?

  • A. -0.70
  • B. +0.11
  • C. +1.46
  • D. -1.19

Solution

The correlation coefficient, often denoted as rr, measures the strength and direction of the linear relationship between two variables. The value of rr ranges from -1 to +1:

  • A correlation of +1 indicates a perfect positive linear relationship.
  • A correlation of -1 indicates a perfect negative linear relationship.
  • A correlation of 0 indicates no linear relationship.

In this context:

  • A. -0.70: Indicates a strong negative linear relationship.
  • B. +0.11: Indicates a very weak positive linear relationship.
  • C. +1.46: This is not a valid value for correlation as rr must be between -1 and +1.
  • D. -1.19: This is also not a valid value for correlation as rr must be between -1 and +1.

Given the valid options, A. -0.70 is the best result, as it has the highest magnitude of correlation (closest to -1 or +1), indicating a stronger linear relationship compared to the other valid option, B (+0.11).

Would you like more details or have any questions?

Here are 5 related questions:

  1. What are the limitations of correlation coefficients?
  2. How does correlation differ from causation?
  3. What is the meaning of a correlation of 0?
  4. What statistical tests are used to determine the significance of a correlation?
  5. How does sample size affect the reliability of a correlation?

Tip: Always check the range of the correlation coefficient to ensure it falls between -1 and +1.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient

Formulas

Pearson Correlation Coefficient (r)

Theorems

Range of Correlation (-1 to +1)

Suitable Grade Level

Grades 10-12