Combining the effect of the linear and the Quadratic terms in Regression

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Hi all,

I am running a poisson regression model where I have linear term and quadratic term of time as predictors. When both are significant, can I combine the 2 B coefficients in one? if yes, should I take the square root first for the quadratic term?

thanks in advance really appreciate your comments and any refernce

[Lazar]

Not sure what you mean but, if intercept is .23, linear beta = .76 and quad beta = .25 then y =.23 + .46*x + .25*x^2.

[duskstar]

You don't need to combine them, just keep both coefficients in and investigate if you need any higher ones.

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Thanks a lot, both of you, for the replay, I thought "maybe" we can combine them and say 1 unit change in x= (B1+B2[Quad.]) change in y? cause both of them are for time and I am interested in knowing how much change in Y happen each year.

[Dason]

The thing is that if there is a quadratic effect then "an increase of one year" isn't enough information to tell you how your prediction will change. Once you add the quadratic effect you have to know which values of the predictors you're talking about to say anything about a predicted change.

For example if our model is:
y = 0 + 1*x + 2*x^2

Then the change from x=0 to x=1 is 3.
The change from x=1 to x=2 is 7.

So we need to know which value of x we're talking about to be able to actually tell you what the predicted change will be.

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Thank you very much