So, the article is about regression analysis: And there when I first studied the topic, I saw the interest in assigning importance to variables one at a time based on the size of their regression coefficients.
Well, there is some math supporting regression analysis if want to use that math, i.e., confirm the assumptions, nearly never doable.
So, I did see that if the independent variables were all orthogonal, this one at a time work had some support. E.g., in linear algebra look at Bessel's inequality.
Otherwise, easily can get confused: So, we're trying to predict Y from U and V. U doesn't do at all well; neither does V, but together U and V predict Y essentially perfectly. How, why? U spans a vector space, and Y is not in that space. We can project Y onto that vector space and have the projection small (coefficient of U small). Same for V. But U and V together span a vector space, one that includes Y -- so U and V predict Y perfectly. Just simple vector space geometry. It can happen.
This stuff about controlling can make some good sense in cross-tabulation (see my post here on that), but in regression analysis? Controlling? Where do they get the really strong funny stuff they've been smoking to believe in that?
Well, there is some math supporting regression analysis if want to use that math, i.e., confirm the assumptions, nearly never doable.
So, I did see that if the independent variables were all orthogonal, this one at a time work had some support. E.g., in linear algebra look at Bessel's inequality.
Otherwise, easily can get confused: So, we're trying to predict Y from U and V. U doesn't do at all well; neither does V, but together U and V predict Y essentially perfectly. How, why? U spans a vector space, and Y is not in that space. We can project Y onto that vector space and have the projection small (coefficient of U small). Same for V. But U and V together span a vector space, one that includes Y -- so U and V predict Y perfectly. Just simple vector space geometry. It can happen.
This stuff about controlling can make some good sense in cross-tabulation (see my post here on that), but in regression analysis? Controlling? Where do they get the really strong funny stuff they've been smoking to believe in that?