In an underdetermined linear regression setup, why does the residual sum of squares equal 0? In an underdetermined linear regression where the parameters to estimate outnumber the observations, why is it the case the residual sum of squares, defined as:
$$
RSS = \sum_{i=1}^n (y_i-\widehat{y}_i)^2
$$
equal zero?

With one predictor (and an intercept): two points determines a lines exactly, with less than two points there are infinitely many lines that pass through that point ...
With two predictors (and an intercept): three points determines a plane exactly, with less than three points infinitely many planes will fit perfectly ...
The same principle continues into higher dimension.
