Hongjie Wang wrote: > > Dear friends: > > Recently, I saw a regression mode y=a x + b (x^2) + some other stuff. > where a and b are two numbers of opposite signs. Does that seem normal? > It is counterintuitive that y is positively related to x and then negatively > related to x^2. > But then, it is multivariate analysis. Any insights will be appreciated.

Y is a quadratic function of x. If the value of b is positive, as you think it should be, then the derivative of the quadratic function will be positive whenever x is positive. Not knowing the problem, I see no a priori reason why the derivative must be positive whenever x > 0. Letting b be < 0 allows negative derivatives of your quadratic function, which seems quite possible to me.

By the way, I do not consider this multivariate analysis. The terminology I am familiar with does not call regression with a single Y variable "multivariate".

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