Hello!
I am analyzing the effect of wind on the fertility rate using a quadratic term of wind:

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I get the following output in stata:

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The utest showed that the inverse U-shape is significant at a 5% level.
Now i wanted to do a robustness check using wind bins of 25kmh, which gives me the following output with a constant of 146.3851:

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Plotting both yields the following graph, where the red parts are significant while the grey ones are nonsignificant.

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Now this shows me, that there is not really a strong U-shape, as some bins in the positive "area" are negative and the other way around. What stands out is that all those bins that break the ranks are insignificant.
So I am confused on how to argue about the results. Can I just ignore the insignificant ones and talk about a U-shape? I have around 90 observations in the first 9 bins, is this maybe too less? I dont know if I can talk about a causal effect in this case. Maybe the only thing that I can really say is that quite low wind speeds increase the fertility rate while really high ones decrease it?
I was also wondering why the graph of the bins is so much higher than the polynomial graph.
So, basically the question is: Does the result of the binning process "destroy" my assumption about the U-shape?

Thank you a lot in advance!