Fast and essential linear regression

Essential, fast and efficient simple linear regression

Essential, fast and efficient simple linear regression implementation.
Returns estimated coefficients and p-values for linear regressions of the form y~a.*X+c.
The function is easy to adapt for returning less simplistic and/or structured outputs.

This is meant to be used e.g. in complex scripts, large-scale problems, or loops, where only the estimates and optionally p-values are of interest. On the contrary, built-in functions like 'fitlm' return complex structs and several additional information that might not be of interest, affecting the execution time.