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# Re: st: significance of the variables based on t-test or f-test

 From László Németh To statalist@hsphsun2.harvard.edu Subject Re: st: significance of the variables based on t-test or f-test Date Mon, 3 Sep 2012 06:07:45 +0200

```Dear Paul and Nick,

thank you very much for your answers. They really helped me a lot in
the interpretation of my results.

Best regards,
László

2012/8/31 Nick Cox <njcoxstata@gmail.com>:
> Paul is absolutely right to underline the correlation between linear
> and quadratic terms, but I would stress with Maarten that plotting of
> the data is surely and sorely needed to get a qualitative
> understanding of whether some kind of curvature is needed or
> justified.
>
> It is my frequent practice to compare a quadratic fit with a
> fractional polynomial (default) fit and a restricted cubic spline fit.
>
> sysuse auto
> scatter mpg weight || lfit mpg weight || qfit mpg weight || fpfit mpg
> weight, ///
> legend(order(1 "data"  2 "linear" 3 "quadratic" 4 "fracpoly"))
>
> For a restricted cubic spline fit, -rcspline- (SSC) is a convenience
> wrapper. My suggestions are that
>
> 1. If qfit, fpfit, rcspline agree, then quadratic is a good model. It
> is not only simple but matches more flexible smoothers. But separate
> testing of linear and quadratic terms makes no sense.
>
> 2. If any two of qfit, fpfit, rcspline disagree strongly, you need to
> think more about what is going on.
>
> Nick
>
> On Fri, Aug 31, 2012 at 9:32 AM, Seed, Paul <paul.seed@kcl.ac.uk> wrote:
>
>> In László's present model, it is likely that the linear and
>> quadratic terms are highly correlated, and the tests
>> do not make sense taken separately.  Hence the need to rely on the
>> F-test for the whole model.  It's weakness suggests nothing much
>> (compared to the size & power of the data set) is going on.
>>
>> Maarten's main conclusion notwithstanding,
>> anyone facing a similar problem to László may wish to
>> look at using orthogonal polynomials (Stata command -orthog-).
>> Reference: Golub, G. H., and C. F. Van Loan. 1996.  Matrix
>> Computations. 3rd ed.  Baltimore: Johns Hopkins University Press.
>> László might also want to do this if cleaning and transforming
>> the data improves the overall F test.
>>
>> A sequence such as the following might show something.
>> Higher degrees can also be used.
>>         orthog xi, poly(xi_) degree(2)
>>         regress y xi_1 xi_2
>
> 2012/8/30 Maarten Buis <maartenlbuis@gmail.com>:
>
>>> The main conclusion is that you cannot reject the hypothesis that
>>> screening intensity is neither linearly nor quadraticly related to
>>>
>>> I would look at a scatter plot of performance against screening
>>> intensity and look if you can see any anomalies. If that does not
>>> work, than you'll just have to live with the fact that your data tells
>>> you that the two are unrelated.
>
> On Wed, Aug 29, 2012 at 6:59 PM, László Németh wrote:
>
>>>> I would like to analyze the relationship between the risk-adjusted
>>>> performance (DV) and the screening intensity of the SRI funds (IV). In
>>>> the first model I assume a linear relationship between these two
>>>> variables:
>>>> y = B0 + B1*xi+ui
>>>> The t-statistic of screening intensity is here 0.84
>>>>
>>>> Then I use a second model, where I add the square of screening
>>>> intensity (Xi2) as a second independent variable: y=B0 +
>>>> B1*xi+B2*xi2+ui
>>>> The t-statistic of Xi is 2.02, whereas the t-statistic of Xi2 -2.17
>>>> is. Based on this results I assume that there is a quadratic
>>>> relationship between the risk-adjusted performance and the screening
>>>> intensity of the funds. However, if I run an F-test with the two
>>>> independent variables I got a p-value of 0.1008.
>>>>
>>>> Now, I am not sure how I should interpret these results. Based on the
>>>> t-statistic, I think that there is a quadratic relationship, but the
>>>> results of the F-test make me uncertain. That is why I would like to
>
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```