Testing a model with linear and quadratic components - advice!

Hi everyone,

I am looking for a second opinion on an analysis I am currently completing. I have three variables, and the hypothesised relationships form a very simple model: var1 -> var2 -> var3

The complexity is that I am hypothesizing that the relationship between var1 and var2 is quadratic.

I have tried testing this initially using a straight mediated regression, saving the residuals of the dependent variables in each step of the regression and then conduting a second mediated regression analysis using the residual variance as the dependent variables and making var1 and quadratic term. The intent is that the linear affect is partialled out and then I am testing to see if the quadratic term accounts for variance in the second analysis. Hope that makes some sense!

Anyway, I am wondering if there is another way this model could be tested, and also whether anyone can explain whether curve estimation would be a good way to test initially whether the relationship between var1 and var 2 is actually quadratic. I have never done that before and am not sure how to use the test.

Any thoughts would be much appreciated!!!

I can't say I fully understand your post, but if you're looking to see if the model should be:

VAR2 = b0 + b1*VAR1 + b2*VAR1*VAR1

that is, you're wondering if the b2 coefficient on the VAR1*VAR1 term is statistically significant, then I believe you would perform a t-test for the b2 coefficient to determine if it should be included in the model.