R 2 Linear Regression Calculator

R² Formula:

\[ R^2 = \frac{\text{Explained Variation}}{\text{Total Variation}} \]

R² Value:

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1. What is R² in Linear Regression?

R² (R-squared) 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. It indicates how well data points fit a statistical model.

2. How Does the Calculator Work?

The calculator uses the R² formula:

\[ R^2 = \frac{\text{Explained Variation}}{\text{Total Variation}} \]

Where:

Explained Variation — The variation explained by the regression model
Total Variation — The total variation in the dependent variable

Explanation: R² values range from 0 to 1, where 0 indicates that the model explains none of the variability and 1 indicates that it explains all the variability.

3. Importance of R² Calculation

Details: R² is crucial for evaluating the goodness of fit of regression models. It helps determine how well the regression predictions approximate the real data points.

4. Using the Calculator

Tips: Enter the explained variation and total variation values. Both values must be positive numbers, with total variation greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a good R² value?
A: Generally, higher R² values indicate better model fit. However, acceptable values vary by field - social sciences may accept lower values (0.3-0.5) while physical sciences often expect higher values (>0.8).

Q2: Can R² be negative?
A: In ordinary least squares regression, R² ranges from 0 to 1. Negative values may occur in other contexts but typically indicate worse fit than a horizontal line.

Q3: What are the limitations of R²?
A: R² always increases with additional predictors, which can lead to overfitting. It doesn't indicate whether regression coefficients are statistically significant.

Q4: How is R² different from adjusted R²?
A: Adjusted R² penalizes for adding unnecessary predictors, providing a more accurate measure when comparing models with different numbers of predictors.

Q5: When should I use R²?
A: Use R² to compare the explanatory power of regression models and to understand how well your model fits the data, particularly in linear regression analysis.