Interpretation of U Shape

[Paul Olz]

After immense looking at the forum and other sources, I was not able to identify guidance for the utest command and especially its interpretation. How do I interpret my results at this point? Are there any further tests I need to conduct?

Thank you very much in advance for your support!!!

[Paul Olz]

Here the output

[Nick Cox]

utest is from SSC. I have never used it, but (I guess that) the help file is terse in the expectation that people will read the paper it references.


Hitherto I have always relied on comparing a linear and a quadratic fit, bearing in mind always that a predictor and its square are usually highly correlated and that working with (predictor MINUS constant) and its square is often a better idea.

[Paul Olz]

Thank you very much for the information, Nick.

One more general, additional question: With the above shown results, I can say that there is a inverse U shape, although the t-value is positive, correct?

[Nick Cox]

Sorry. but I haven't studied this command or the paper behind it in detail. But I would always plot the quadratic if I were in doubt.

Silly example:

sysuse auto, clear

gen weightsq = weight^2
regress mpg c.weight##c.weight
regress mpg weight weightsq

twoway function _b[weight] * x + _b[weightsq] * x^2 , ra(weight)