1. What is Correlation of Determination?

The correlation of determination (r²) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( r \) — Correlation coefficient (ranges from -1 to 1)
• \( r^2 \) — Coefficient of determination (ranges from 0 to 1)

Explanation: The coefficient of determination shows how well data points fit a statistical model - either a line or a curve.

3. Importance of r² Calculation

Details: r² is crucial in regression analysis as it indicates the proportion of variance in the dependent variable that is predictable from the independent variable(s).

4. Using the Calculator

Tips: Enter correlation coefficient (r) value between -1 and 1. The calculator will square this value to give you r².

5. Frequently Asked Questions (FAQ)

Q1: What does an r² value of 0.8 mean?
A: It means 80% of the variance in the dependent variable is predictable from the independent variable.

Q2: Can r² be negative?
A: No, r² ranges from 0 to 1 because it's a squared value.

Q3: What's the difference between r and r²?
A: r measures the strength and direction of a linear relationship, while r² measures how much variance is explained.

Q4: Is higher r² always better?
A: Not necessarily. Very high r² might indicate overfitting in predictive models.

Q5: What's a good r² value?
A: It depends on the field of study. In social sciences, 0.3 might be acceptable, while in physics 0.9+ might be expected.