# R-Squared (R²)

## Description

Known as the coefficient of determination, R² identifies how well the predictions performed by the model fit (match) the acutual data. On a scale of 0 to 1, the strength of the relationship between the model and the actual data will be measured. However, it does not tell you whether your model is correct or meaningful. The R² is defined as:

\[\text{R²} = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2}\]

where:

( n ) is the number of observations.

( y_i ) is the actual value.

( hat{y}_i ) is the predicted value.

( bar{y} ) is the mean of the actual values.

## Tools and Libraries

### Python

To compute the R² between the actual values and predicted values, the following example can be used.

Install **scikit-learn** via this command:

```
pip install -U scikit-learn
```

```
from sklearn.metrics import r2_score
y_true = [5, 0.2, 8, -0.3]
y_pred = [6, 0.0, 7, 0.0]
R_Squared = r2_score(y_true, y_pred)
print(f"The R² is: {R_Squared}")
```