Ethan's Notes

    Coefficient Of Determination

    #Math

    $\displaystyle R^{2}=1- \frac{\sum_{i}(\hat{y}{i}-y{i})^{2}}{\sum_{i}(\bar{y}-y_{i})^{2}}$

    • $\displaystyle \hat{y}{i}$ is the predicted value of $\displaystyle y$ due to a point $\displaystyle x{i}$
    • The numerator term is the sum of squares of residuals, or a sort of error of the model
    • The denominator term is the total sum of squares, or a sort of error of the average
    • The denominator
    • Ranges from $\displaystyle 0$ to $\displaystyle 1$
      • $\displaystyle R^{2}=1$ means total correlation between our predictor variable and our response variable