🚀 go-pugleaf

>>Why don't you try calculating the correlation coefficient: the closer it
>>is to 1 or -1, the more linear your data.

>I do not think that the corr. coef. would tell much at all right away.    
>If he is asking about linearity I'm sure he has in mind fitting a straight 
>line.
>He says:  

>>" I have a question regarding, linearity
>>of data points.  Does anybody know of any statistical
>>test for linearity. I would appreciate any kind of
>>help, references etc."

>I would think that PLOTTING the data first would be necessary in order 
>to asses the rest of the test:

>ie:if there is a pattern other than some kind of random scattering along some
>invisible straight line (ie: curvilinear like a parabola) then he should fit
>a polynomial model (possibly of second order), then the reduced model with 
>only the linear term and THEN asses linearity by means of the corresponding 
>tests.
I agree.   Actually testing the correlation is already assuming that 
linearity exists (a constant change in y per unit change in x) and the 
correlation test is a hypothesis that the slope (constant change in y) 
is equal to zero.  Working with a model not assuming linearity (one with 
linear and  quadratic and cubic components) and then testing a linearity 
restriction would seem much more in order since linearity technically
can exist when the slope is equal to zero.  Once you've then assumed 
linearity you may want to test that the slope is zero (where the 
restricted model has only an intercept term as a predictor).  Accepting
this model might suggest that the functional form of y is more complex
than fitting any of the models thus far or that their is no relationship
at all.

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Richard Cole, Stat/Math Services         Learning to  
Computation Center UT Austin TX, 78712   Paint by 
rcole@ccwf.cc.utexas.edu                 Numbers 
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