# Given a dependent variable how can I determine the relative effect of several independent variables to its value?

Say I have a series of N observations, and for each observation, I have 4 variables: $$x$$, $$y$$, $$z$$, and $$q$$, where $$q$$'s value depends on at least two of the other variables.

How can I establish the extent to which each of these variables contributes to the value of $$q$$?

The observations take the form $$x_n$$, $$y_n$$, $$z_n$$, $$q_n$$, where $$x_n$$ is the $$n$$th value of $$x$$. I'm looking for the overall contribution of $$x$$, $$y$$ and $$z$$ based on the whole series.

• In one sense, this is what regression does, but only in a qualified sense. Only if the predictors (features) have completely separate contributions can relative importance be determined clearly. You can get some sense of relative importance through how well 1, 2, 3, 4 predictors work, there being 15 possible regressions. The terms dependent and independent variables refuse to die, but there are any number of better terms available. Machine learning terminology can differ from that in mainstream statistics. , Apr 10 at 13:53
• Thanks @NickCox. I wondered if something like a regressive neural net could be used to predict q, having been trained on prior input vectors of x, y, z, with output q. What I'm not clear on is how to establish weightings for x, y, z. In particular, I know that one of these input features may have no effect on q.
– j b
Apr 10 at 16:11
• Indeed; quite how to do is up for grabs. But whether all four predictors improve on just three in prediction is one measure of how important the fourth is. But the whole exercise will be a team effort that can't be divided into separate credit for the players. Apr 10 at 16:56