Coefficient of Determination

$R^2=1-\frac{{\sum }_i({\hat{y}}_i-y_i{)}^2}{{\sum }_i(\bar{y}-y_i{)}^2}$

• ${\hat{y}}_i$ is the predicted value of $y$ due to a point $x_i$
• 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 $0$ to $1$
  • $R^2=1$ means total correlation between our predictor variable and our response variable