1. What Is The Linear Correlation Coefficient?

The Pearson linear correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates perfect negative correlation, +1 indicates perfect positive correlation, and 0 indicates no linear correlation.

2. How Does The Calculator Work?

The calculator uses the Pearson correlation formula:

Where:

• \( r \) — Pearson correlation coefficient (dimensionless)
• \( Cov(X,Y) \) — Covariance between variables X and Y
• \( \sigma_x \) — Standard deviation of variable X
• \( \sigma_y \) — Standard deviation of variable Y

Explanation: The formula standardizes the covariance by dividing by the product of the standard deviations, resulting in a dimensionless measure between -1 and +1.

3. Importance Of Correlation Analysis

Details: Correlation analysis is fundamental in statistics for identifying relationships between variables, guiding further analysis, and informing decision-making in research, business, and scientific studies.

4. Using The Calculator

Tips: Enter the covariance between X and Y, and the standard deviations for both variables. All values must be valid (standard deviations > 0). The result is dimensionless and ranges from -1 to +1.

5. Frequently Asked Questions (FAQ)

Q1: What does the correlation coefficient value mean?
A: Values close to +1 indicate strong positive correlation, close to -1 indicate strong negative correlation, and values near 0 indicate weak or no linear correlation.

Q2: Can correlation imply causation?
A: No, correlation does not imply causation. A strong correlation between two variables does not mean that one causes the other.

Q3: What are the assumptions for Pearson correlation?
A: Variables should be continuous, linearly related, approximately normally distributed, and have homoscedasticity (constant variance).

Q4: When should I use other correlation measures?
A: Use Spearman's rank correlation for ordinal data or when assumptions of Pearson correlation are violated, and point-biserial correlation for one continuous and one dichotomous variable.

Q5: How do I interpret the strength of correlation?
A: Generally: ±0.00-0.19 (very weak), ±0.20-0.39 (weak), ±0.40-0.59 (moderate), ±0.60-0.79 (strong), ±0.80-1.00 (very strong).