My understanding of a quadratic term in a regular regression is that it can be thought of as the rate of change, where the slope in the original feature x is adjusted by the amount in the quadratic term for each additional unit of x.
E.g. In a regular regression if age in years is associated with an increase in y of 10 and age ^2 is 2 then after 10/2 = 5 years the affect of age is doubled to +20 on y.
Have I understood the linear regression case correctly?
If so, how should I interpret a quadratic term for a logistic regression? If I have a feature x with a logit estimate of -0.010415882669274, and odds ratio of 0.242703979997507 and the corresponding values for the quadratic term of 0.0000903917003615193 for the logit estimate and 1.00009039578581 for the odds ratio.
How can I interpret the quadratic effect of x on y?
