interpreting a model after mean centering

#1
hello,

I have to choose the best way to model the relationship between years' experience and time taken to master a new skill. The curve seems to be quadratic, and a quadratic model does have a very high r^2 (over .90). However, as is common in polynomial regression, there is a high degree of multicollinearity. So I corrected for this using mean centering (taking from experience its mean; and then calculating experience^2 by squaring the new mean centered variable). This reduced multicollinearity.
However my problem is then how to describe the model. Normally I would write, the model is, as below, where y = time taken to master the skill (hours) and x = experience (years). However, how would one do this following mean-centering?
would you write, where x is experience in years mean-centered? and what about y?

many thanks
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
You only mention one dependent variable, where is the multicollinearity. I could be wrong, but I usually only think of multicollinearity between two dependent variables.

Are there other variables that you are not mentioning?
 
#3
sorry I mean as in multicollinearity between the predictor variables (experience and experience squared), that is how I understand multicollinearity...
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
Gotcha, you have two independent variables based on the same variable. If the response seems quadratic and the model explains much of the variance, why not just use y = X^2?
 

Dason

Ambassador to the humans
#7
Are you implying that they drop the constant and the linear term? Or just that they don't mean center?
 
#8
it is the quadratic equation itself, in the form y=a+bx+bx^2 that yields the high r^2 value, y=x^2 in itself can only account for approx. 50% of the variance in y.
I was just interested in how to interpret this model following mean centering. thanks for your responses
 

hlsmith

Less is more. Stay pure. Stay poor.
#9
I guess why mean center, the only risk with the collinearity is inflated variance and the model is explaining > 90%. Though, this seems to be an example and exploratory so I guess if they can explain the centered mean (which I cannot remember the specific of too much right now).