How are the critical value (F statistic) and the p-value in regress calculated?

Hi. I am running a multiple regression analysis with [b,bint,r,rint,stats] = regress(y,X). Regarding 'stats' I have the following questions: 1) What is the critical value (alpha) for the F statistic? I mean which value does Matlab 'assume' (e.g. alpha=0.01, alpha=0.05...)? 2) How does Matlab compute the p-value? The p-value(which should be smaller than the critical value of the F statistic in order to have a significant test) is normally the area beneath the right tail of the f distribution at the F-value, if I understood the concept correctly. With respect to the regress command - does Matlab simply calculate this area or does it calculate the p-value differently?

Thank you!

Answer 1

[the cyclist]

As stated in "help regress", the default test is at the 95% confidence level (i.e. alpha=0.05). You can also use a third input argument to specify a different value of alpha.

Yes, MATLAB calculates the area under the F cumulative distribution function.

[Alwin]

Thanks, that helped a lot. Could you please explain how you would change the confidence interval/alpha?

[Oleg Komarov]

Please read the documentation of the function, it's immediately there: http://www.mathworks.co.uk/help/toolbox/stats/regress.html

Also, accept his answer if you believe your questions were answered.

[the cyclist]

Using random x and y values,

[b,bint,r,rint,stats] = regress(rand(3,1),[ones(3,1),rand(3,1)],0.01)

will calculate intervals with alpha=0.01.

[Alwin]

Great. Sorry for not accepting the answer earlier, but I am kind of new here and with Matlab.