Putting quadratic effect into regression model So I have a least squares model which tries to identify changes in income due to different levels of experience, education, etc. 
But in my model the dependent variable is 'income' and among the independent variables i have 'experience' en the square of 'experience'. When asking the summary of the model, both variables are significant but experience has a positive impact on the income, while the quadratic effect has a negative impact on one's income. Can someone help me in interpreting this, as I find it somehow contradicting..
 A: Depending on the magnitudes of the coefficients (which you did not provide) the fitted curve may be ever-increasing over the range of your data.  The answer comes not in examining the two coefficients but in plotting the fitted curve.  And if a quadratic fit is adequate (often it is not as good as using a regression spline) the estimated vertex of the fitted parabola is $\frac{-b}{2a}$ if the equation is $y = ax^{2} + bx + c$.  Hopefully the vertex is outside the range of education in your sample.
A: The point is that experience ($E$) and experience-squared ($E^2$) are not 'independent'. You seem to reason as if they are: you say that the coeffcient of $E$ is positive while the one of $E^2$ is negative and the latter seems strange to you.  
So your reasoning seems to be that, if $E^2$ increases by one unit then the income decreases by the coefficient of $E^2$. This would be the case, but only if you keep ''all other things equal''. 
But you can not keep all other things equal: if you increase $E^2$ by one unit, then you will also increase $E$ by one unit, so you can only change $E^2$ and not keep ''all other independent variables'' equal; if you change $E^2$ you also change $E$ !
So you can only talk about the impact of experience $E$ on income and that impact has two components: (a) the positive impact via $E$ and (b) the negative impact via $E^2$. But you can not ''talk about'' the impact of $E^2$ only, you see what I mean ?
