1. What is the Coefficient of Determination?

The coefficient of determination (r²) is a statistical measure that represents the proportion of the variance in the dependent variable that's predictable from the independent variable(s). It ranges from 0 to 1, with higher values indicating better fit of the model.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

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

Explanation: The coefficient of determination is simply the square of the correlation coefficient (r). It explains what proportion of the variance in one variable can be explained by the other variable.

3. Importance of r² Calculation

Details: The r² value is crucial in regression analysis as it indicates how well data points fit a statistical model. It helps determine the strength of the relationship between variables.

4. Using the Calculator

Tips: Enter the correlation coefficient (r) value between -1 and 1. The calculator will compute r² automatically.

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 the proportion of variance explained.

Q4: Is higher r² always better?
A: Not necessarily. Very high r² might indicate overfitting, and context matters in interpretation.

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.