I am working with a regression with an x and x squared predictors. The equation is:
-0.0104x + (-0.00002)x^2.
I understand the marginal effect is calculated by differentiating to:
-0.0104 + 2(-0.00002)x, and that the ME is calculated generally at the mean of x.
However, I was also taught that given an x such as 10, one can simply insert 10 in the equation, so that y hat when x is 10 is -0.0104(10) + (-0.00002)(100).
Doing so, I get -0.106. But the marginal effect at 10 is -0.0108.
So there are two values: -0.106, and -0.0108. What is the interpretation of the first value, given the second value is the marginal effect. Is it correct that the marginal effect represents the slope of the inverse parabola at point x=10?