Dear Statalist members,

I have a panel dataset where my dependent variable is a dummy = 1 if the client switches to using self-directed investing, 0 otherwise. My independent variables are performance ratio and the cumulative percentage of using automation.

Code:
g PercentAutoBid_2= PercentAutoBid*PercentAutoBid

        eststo: reghdfe Auto2Man l.performance_ratio l.PercentAutoBid l.PercentAutoBid_2 ///
            ,a(`fe') cluster(interaction)
I want to check whether to include squared term in my regression so I run nlcom

Code:
        nlcom -_b[l.PercentAutoBid]/(2*_b[l.PercentAutoBid_2])

------------------------------------------------------------------------------
    Auto2Man | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .4370262   .0009158   477.22   0.000     .4352314    .4388211
------------------------------------------------------------------------------
The results show me that the coefficient (0.43) lies between the range of PercentAuto. Percent auto is from 0 to 1. which means that I have an inverted U shape right?

then I run the margins command

Code:
        margins, at(l.PercentAutoBid = (0(0.2)1))
        marginsplot
And I get this result
Array


Can someone help me whether I should include a squared term or not?

Thanks