# interpreting a model after mean centering

#### gooner8

##### New Member
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.
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?

#### gooner8

##### New Member
sorry I mean as in multicollinearity between the predictor variables (experience and experience squared), that is how I understand multicollinearity...

#### Englund

##### TS Contributor
What is the purpose of the model? Do you want to use the model for prediction or simply as an explanatory model?

#### gooner8

##### New Member
just to show what the relationship is between the variables, so presumably just an explanatory model.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
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
Are you implying that they drop the constant and the linear term? Or just that they don't mean center?

#### gooner8

##### New Member
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.
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).