Hi, I am conducting an analysis using a robust linear model. I was wondering if it was statistically sound to graph my predicted outcome and then take use the % change in each estimate to address the impact from the x to the y?
If you model log(y) = b0 + b1*x, then b1 estimates the relative change in y per unit change in x. If you model log(y) = b0 + b1*log(x), b1 estimates the relative change in y per relative change in x (in econometrics this is known as the "elasticity" coefficient).
The graphing has little, or nothing, to do with the impact of x on y. The regression coefficient itself, the b, is the impact (i.e. change) in y following a one unit increase in x.
so graphing the prediction by changes in the equations input is statistically sound. For instance, the change between y = b0+b1(x) and y = b0+b1(a) would be the graphed as a % change between the two predictions x and a ?
Jochen Wilhelm is correct. This link may help you see why: https://www.google.com/search?client=firefox-b-1-d&ei=kGTMX-DZDZeztAaqspr4DQ&q=what+is+the+meaning+of+percent+change&oq=+meaning+of+percent+change+&gs_lcp=CgZwc3ktYWIQARgBMgQIABAeMgYIABAFEB4yBggAEAUQHjIGCAAQCBAeOgQIABBHOggIIRAWEB0QHjoJCAAQyQMQFhAeOgYIABAWEB46CAgAEAgQChAeOgYIABAHEB46BAgAEEM6BQgAEJECOgUIABCxAzoICAAQsQMQgwE6DAgAEMkDEEMQRhD5AToECAAQDToCCAA6BQgAEMkDOggIABAIEAcQHjoICAAQBxAFEB5QjO8LWK-dDWDgmw5oAHACeACAAbQBiAHeHpIBBTE2LjIwmAEAoAEBqgEHZ3dzLXdpesgBCMABAQ&sclient=psy-ab
Best, David Booth
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