2
votes
1answer
110 views

Applying ridge regression for an underdetermined system of equations?

When $y = X\beta + e$, the least squares problem which imposes a spherical restriction $\delta$ on the value of $\beta$ can be written as \begin{equation} \begin{array} &\operatorname{min}\ \| y - ...
2
votes
0answers
49 views

Interpretation of regression coefficients obtained from applying left inverse of regressor matrix in an underdetermined system?

If $X^\dagger$ is the pseudo-inverse of $X$, $\beta = X^\dagger y$ is the least squares solution for $\beta$ when $y=X\beta$. In the overdetermined case, applying $X^{\dagger,L} = (X^TX)^{-1}X^T$ ...
17
votes
5answers
2k views

Detecting significant predictors out of 300 independent variables

In a dataset of two non-overlapping populations (patients & healthy, total $n=60$) I would like to find (out of $300$ independent variables) significant predictors for a continuous dependent ...