This is a linkpost for https://putanumonit.com/2017/03/12/goddess-spreadsheet/
Excellent post on exactly the topic it suggests. And putting a number on it (WRT relationship values). And a happy success story.
I didn't actually do linear regression for the girlfriend matrix, but in general I use the glm function in R. It allows you to quickly generate regression models with any combination of variables by changing a couple of words, and saves the full model for analysis and manipulation.
If you don't need to compare different models (e.g. to pick out which variable are useful and which are just noise), you can even run a regression in Excel (Data -> Data Analysis). If you don't want to install any software at all, Wolfram Alpha got you covered.