Is there any Interpretation to be drawn if the squared term is significant but the term with power 1 is not?

[David Kang]

Hello,

In one of my regressions the age variable is positive and not significant, but the age^2 variable is negative and very significant.

Do I abstain from interpreting the effect of age completely? Or do I simply assert that there is a likelihood of diminishing returns of age on variable Y.

[Clyde Schechter]

In a quadratic model, the statistical significance of the linear or quadratic term by itself is completely meaningless and should not even be looked at!

If you feel you must look at the statistical significance of an age effect, do so by testing them jointly:

test age c.age#c.age

Note: The above code assumes you used factor variable notation for your quadratic term. If you didn't, I recommend you go back and redo the regression that way. -help fvvarlist- if you are not familiar with factor variable notation.

The best way to interpret quadratic models is to look at the graph. Let's say age runs from 20 through 80 in your data

margins, at(age = (20(5)80))
marginsplot

That picture should feed your understanding of the role that age is playing your model. If you wish to write 1,000 or fewer words describing it, go ahead.

[David Kang]

In a quadratic model, the statistical significance of the linear or quadratic term by itself is completely meaningless and should not even be looked at!

If you feel you must look at the statistical significance of an age effect, do so by testing them jointly:

test age c.age#c.age

Note: The above code assumes you used factor variable notation for your quadratic term. If you didn't, I recommend you go back and redo the regression that way. -help fvvarlist- if you are not familiar with factor variable notation.

The best way to interpret quadratic models is to look at the graph. Let's say age runs from 20 through 80 in your data

margins, at(age = (20(5)80))
marginsplot

That picture should feed your understanding of the role that age is playing your model. If you wish to write 1,000 or fewer words describing it, go ahead.

Sorry, both terms are included in the regression, but only age^2 is significant. My question is can you draw any interpretation from that

[Clyde Schechter]

I tried to answer that question in #2 in my very first line "In a quadratic model, the statistical significance of the linear or quadratic term by itself is completely meaningless and should not even be looked at!", but apparently I didn't succeed. The short version is: no, you cannot draw any conclusions from that.

[Richard Williams]

I'll just add that there is nothing that says that the coefficient for age can't be zero while the coefficient for age^2 is nonzero. It would almost certainly be a mistake to drop age while leaving age^2 in. In general, if higher-level terms (e.g. interactions, squared terms) are in a model, lower level terms (including terms used to compute interactions) should be left in even if they are insignificant.