Regression Model Evaluation

• One of the key aspects of supervised machine learning is model evaluation and validation.
• Two popular measures of evaluation

Coefficient of Determination

• Measures the proportion of variance in the target variable that is explained by the model
  • The best possible score for $R^2$ is 1.0 (when $u=0$)
  • Lower values are worse
  • $R^2$ is 0.0 when $u=v$
  \begin{aligned} R^2 = (1 - \frac{u}{v})\\ 0 <= R^2 <= 1 \end{aligned} $$ - Where: - the term $u$ is the **residual sum of squares** $$ u = \sum (y - \hat y)^2 $$ - $y$ is the **observed response** - $\hat y$ is the **predicted response** - the term $v$ is the **total sum of squares** $$ v = \sum (y - \bar y)^2 $$ - $\bar y$ is the **mean of the observed data**

Mean Squared Error ($MSE$)

• Measures average squared difference between actual and predicted values
  • Lower MSE = better predictions

IMPORTANT

It’s an absolute error metric → the smaller, the better

$$
MSE = \frac{1}{n} \sum (y - \hat y)^2
$$

• Where:
  • the term $n$ is the total number of observations in the dataset