I'm working on a promotional response analysis. I have a **really small** real world dataset with 25 observations and 15 variables. The variables have a **high degree of multicollinearity** and some have **outliers**. Also, I cannot use machine learning methods because I need interpretable coefficients.

Here is what I have tried so far: 

1. I used GLM, but all variables seemed insignificant. I know for a fact that the dependent variable is responsive to many independent variables.
2. I used robust regression, but basically the program fails because the software showed an error that stated, "The number of observations must be at least twice the number of coefficients."

I would really appreciate if you could suggest some methods/techniques or strategies to solve this problem. Thanks and regards.