Question about the Total, Explained, and Residual Sum of Squares. I am in the simple linear regression model.
Could you help me clarify why the residual sum of squares (SSE where E stands for errors)
$$SSE = \sum_{i=1}^n (\hat{Y}_{i}-Y_{i})^{2} $$
is the amount in variance of Y which is not explained by the model and why the explained sum of squares (SSR where R stands for regression)
$$SSR = \sum_{i=1}^n (\hat{Y}_{i}-\bar{Y})^{2} $$
is the amount in variance of Y which is explained by the model, where $Y_{i}$ are the observations, $\bar{y}$ is the esperance and $\hat{Y}_{i}$ are the predicted values in the model.