R Squared Calculation by Hand
Introduction & Importance
R-squared, also known as the coefficient of determination, 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.
How to Use This Calculator
- Enter the Sum of Squares (SS) and Total Sum of Squares (TSS) values.
- Click ‘Calculate’.
- View the R-squared value and a visual representation in the chart.
Formula & Methodology
The formula for R-squared is:
R² = 1 – (SS / TSS)
Real-World Examples
Example 1: Weather Data
Suppose we have weather data where temperature (T) is the dependent variable and humidity (H) is the independent variable. After running a regression, we find SS = 100 and TSS = 200.
R² = 1 – (100 / 200) = 0.5 or 50%
Example 2: Sales Data
In a sales dataset, sales (S) is the dependent variable and advertising spend (A) is the independent variable. After running a regression, we find SS = 500 and TSS = 1000.
R² = 1 – (500 / 1000) = 0.5 or 50%
Data & Statistics
| SS | TSS | R² |
|---|---|---|
| 100 | 200 | 0.5 |
| 500 | 1000 | 0.5 |
| SS | TSS | R² |
|---|---|---|
| 200 | 400 | 0.5 |
| 800 | 1600 | 0.5 |
Expert Tips
- R-squared values range from 0 to 1. A higher value indicates a better fit of the regression model.
- R-squared alone is not enough to judge a model’s goodness of fit. Consider other metrics like adjusted R-squared and residual analysis.
Interactive FAQ
What does R-squared measure?
R-squared measures the proportion of the variance in the dependent variable that’s explained by the independent variable(s) in a regression model.
What does a high R-squared value mean?
A high R-squared value indicates that the regression model explains a large proportion of the variance in the dependent variable.