Calculate R And R2 Calculator

Correlation Coefficient Formula:

\[ R = \frac{Cov(X,Y)}{\sigma_x \sigma_y} \] \[ R^2 = R \times R \]

Correlation Coefficient (R):

Coefficient of Determination (R²):

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1. What is R and R²?

R (correlation coefficient) measures the strength and direction of the linear relationship between two variables. R² (coefficient of determination) represents the proportion of variance in the dependent variable that's predictable from the independent variable.

2. How Does the Calculator Work?

The calculator uses the correlation coefficient formula:

\[ R = \frac{Cov(X,Y)}{\sigma_x \sigma_y} \] \[ R^2 = R \times R \]

Where:

\( Cov(X,Y) \) — Covariance between variables X and Y
\( \sigma_x \) — Standard deviation of variable X
\( \sigma_y \) — Standard deviation of variable Y

Explanation: The correlation coefficient ranges from -1 to +1, where -1 indicates perfect negative correlation, +1 indicates perfect positive correlation, and 0 indicates no linear correlation.

3. Importance of Correlation Analysis

Details: Correlation analysis helps identify relationships between variables, but it's important to remember that correlation does not imply causation. R² indicates how well the independent variable explains the variation in the dependent variable.

4. Using the Calculator

Tips: Enter the covariance between X and Y, and the standard deviations for both variables. All values must be valid numerical values with standard deviations greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a high R value indicate?
A: A high absolute R value (close to ±1) indicates a strong linear relationship between the variables.

Q2: How is R² interpreted?
A: R² represents the proportion of variance explained. For example, R² = 0.80 means 80% of the variance in Y is explained by X.

Q3: Can correlation imply causation?
A: No, correlation only measures association. Causation requires additional evidence from controlled experiments or theoretical justification.

Q4: What are the limitations of correlation analysis?
A: Correlation only measures linear relationships, can be influenced by outliers, and doesn't account for confounding variables.

Q5: When should I use this calculator?
A: Use this calculator when you have calculated covariance and standard deviations separately and want to determine the correlation coefficient and coefficient of determination.