I have a number of independent variables $x_1,x_2,...,x_m$ and a dependent variable $y$. My dataset contains some million of rows.
Bear with me if my wording is not precise here, and you are welcome to correct me! I assume that there is no multicollinearity in my data, i.e. $x_i$ cannot be explained by $x_j$ for $i\neq j$.
However, the dependent variable $y$ seems to react similarly on changes of, say, $x_1$ and $x_2$. How is it called, if the change in $x_1$ changes $y$ similarly like a change in $x_2$?
The question here is: Being on the greater search for a way to aggregate my $x_i$ to fewer variables, what would be the right method/procedure/research area/search engine term to find out whether (and how) $x_1$ and $x_2$ explain $y$ similarly?