Desmos Correlation Coefficient Calculator

Pearson Correlation Coefficient Formula:

\[ r = \frac{\sum((x_i - \bar{x})(y_i - \bar{y}))}{\sqrt{\sum(x_i - \bar{x})^2 \cdot \sum(y_i - \bar{y})^2}} \]

Correlation Coefficient (r):

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1. What is the Pearson Correlation Coefficient?

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

2. How Does the Calculator Work?

The calculator uses the Pearson correlation formula:

\[ r = \frac{\sum((x_i - \bar{x})(y_i - \bar{y}))}{\sqrt{\sum(x_i - \bar{x})^2 \cdot \sum(y_i - \bar{y})^2}} \]

Where:

\( x_i, y_i \) — Individual data points
\( \bar{x}, \bar{y} \) — Means of x and y values
\( \sum \) — Summation across all data points

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

3. Importance of Correlation Analysis

Details: Correlation analysis helps identify relationships between variables, predict trends, and understand data patterns in fields like statistics, economics, social sciences, and research.

4. Using the Calculator

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

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 close to 0 indicate weak or no correlation.

Q2: Can correlation imply causation?
A: No, correlation only measures association. It does not prove that one variable causes changes in another.

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

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.

Q5: How many data points are needed?
A: Generally, at least 30 pairs are recommended for reliable results, though more complex relationships may require more data.