Multi-Variate linear modeling: how to calculate mathematically vs brute force genetic optimization

I have a hand full of daily economic data. I am currently using a brute force approach. Genetic optimization is only used when k is very large. This method is beautiful to me, but isn't valuable compared to OLS models.

So I have found a set of slides from a .edu source on bi-variate x parameters for estimating y for linear modeling. This is very nice and all but I have far more than two economic indicators in mind. The paper mention linear algebra as being a pre-requisite to much higher k values for "hyperplane" models.

Could anyone provide insight on how this could be done? I am thinking perhaps 10 or 15 x values and a single y value. It would be nice if there where a stupid simple explanation and a highly technical one. Despite a 120-130 IQ in mathematics, I suffer severe ADHD+ASD so learning is hard. :(

Re-stating the Question:

How to perform multi-variate linear regression for k explanatory variables. Where k is an integer element of [1,infinity)

• Also, I am 17, never taken a formal statistics class. I have only watched college lectures on youtube. Commented Aug 9, 2017 at 18:17
• If anyone is curious the gene optimization is for r^2 value of estimate y vs actual y. It seemed the most logical parameter. Kurtosis may be another parameter to optimize amongst the top x percentile of all r^2 values. Haven't tried that one. Commented Aug 9, 2017 at 18:21
• Mathematically this would require some knowledge of algebra (computation of the pseudo-inverse of a matrix). That being said it's implemented in most programming language so I guess you could use it without knowing how it works although this is not always the best idea. The problem you'll have is then how to keep only the most 'relevant' predictors (see feature selection methods e.g. LASSO) or to at least reduce the dimension of the predictors space before hand to avoid using all your computational resources (PCR, PLS etc.). Anyway all of this requires linear algebra... so start with that! Commented Aug 10, 2017 at 7:39
• Also, while a little too basic (no offense meant), I think your question is better suited from CrossValidated stackexchange. Commented Aug 10, 2017 at 7:40
• @Quantuple, none taken. I will place any future questions of this nature on cross validated. Commented Aug 11, 2017 at 20:37