Definition
The correlation coefficient is a statistical measure reflective of the degree to which two variables fluctuate together. The most common correlation coefficient is the Pearson correlation, which measures linear relationships between variables. Its values range between -1 and +1:
- +1 indicates a perfect positive relationship: as one variable increases, the other reliably increases.
- -1 represents a perfect negative relationship: as one variable increases, the other reliably decreases.
- 0 denotes no linear relationship between the variables.
Types of Correlation Coefficients
- Pearson Correlation Coefficient: Measures linear relationships between variables.
- Spearman’s Rank Correlation Coefficient: Assesses monotonic relationships, useful when variables are not normally distributed.
- Kendall’s Tau: Measures ordinal associations, less sensitive to skewed distributions.
Examples
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Study of Exercise and Weight Loss: Suppose a study aims to understand the relationship between hours of exercise per week and weight loss in kilograms. A Pearson correlation coefficient of -0.75 might indicate a strong negative correlation—meaning greater exercise is generally associated with greater weight loss.
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Advertising Spend and Sales Revenue: A company evaluates the relationship between its advertising budget and sales revenue. A correlation coefficient of +0.80 might suggest a strong positive correlation—implying higher advertising spends correspond to increased sales revenue.
Frequently Asked Questions (FAQs)
What does a positive correlation coefficient mean?
A positive correlation coefficient signifies that as one variable increases, the other variable tends to increase as well.
Can the correlation coefficient be greater than 1?
No, the correlation coefficient ranges from -1 to +1. Values outside this range indicate a calculation error.
Is a zero correlation coefficient indicative of independence?
A zero or near-zero correlation coefficient indicates no linear relationship between variables, but they may still be related in a non-linear manner.
How do you interpret a negative correlation coefficient?
A negative correlation coefficient suggests an inverse relationship: as one variable increases, the other decreases.
What is the main difference between Pearson and Spearman’s correlation coefficients?
Pearson’s correlation assesses linear relationships and assumes normally distributed variables, while Spearman’s rank correlation evaluates monotonically increasing/decreasing relationships and handles non-parametric data.
Related Terms
- Regression Analysis: A set of statistical processes for estimating relationships among variables.
- Covariance: A measure of the joint variability of two random variables.
- Standard Deviation: A measure of the amount of variation in a set of values.
- P-value: The probability that the observed results occurred by chance.
Online References
- Investopedia on Correlation Coefficient
- Wikipedia on Correlation Coefficient
- Khan Academy on Correlation and Causality
Suggested Books
- “Statistics for Business and Economics” by Paul Newbold, William L. Carlson, and Betty Thorne
- “The Elements of Statistical Learning” by Trevor Hastie, Robert Tibshirani, and Jerome Friedman
- “Applied Multivariate Statistical Analysis” by Richard A. Johnson and Dean W. Wichern
Fundamentals of Correlation Coefficient: Statistics Basics Quiz
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