1. What is the Sample Correlation Coefficient R?

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

2. How Does the Calculator Work?

The calculator uses the correlation coefficient formula:

Where:

• \( x, y \) — Individual data points
• \( \bar{x}, \bar{y} \) — Means of x and y variables
• \( n \) — Number of data pairs
• \( SD_x, SD_y \) — Standard deviations of x and y

Explanation: The formula calculates how much two variables change together relative to how much they vary individually.

3. Importance of Correlation Coefficient

Details: Correlation coefficient is essential in statistics for identifying relationships between variables, but it's important to remember that correlation does not imply causation.

4. Using the Calculator

Tips: Enter comma-separated values for both X and Y variables. Ensure both lists have the same number of values. The calculator will compute means, standard deviations, and the correlation coefficient.

5. Frequently Asked Questions (FAQ)

Q1: What does a correlation coefficient of 0.8 mean?
A: A correlation of 0.8 indicates a strong positive linear relationship between the two variables.

Q2: Can correlation be negative?
A: Yes, negative correlation (-1 to 0) means as one variable increases, the other tends to decrease.

Q3: What's the difference between correlation and causation?
A: Correlation measures association, while causation implies one variable directly affects the other. Correlation does not prove causation.

Q4: When should I use this calculator?
A: Use it when you want to measure the strength and direction of linear relationship between two continuous variables.

Q5: What are the limitations of correlation coefficient?
A: It only measures linear relationships, can be influenced by outliers, and doesn't indicate the slope of the relationship.