Multivariate results interpretation

Question

Hi JMP experts!

I have a question about how to interpret multivariate results: say I have a data set y, x1, x2 three colums. I try to answer the question whether y is correlated with x1, or x2 or both. I have got Rsquares values and correlation probability both in 3 by 3 matrix form from JMP. The question is whether should I use the probability value to answer the question, or should I use the Rsquare value to answer the qhuestion?

I have got the Rsquare values in the range of 0.2 ~ 0.4, but probability values very small (<0.01). Do these results answer the question of their correlation?

I have also used "Fit Model"  and the results show very low probability on x1 (Prob > |t|), but very high probability on x2.

Should I expect consistency by using the two methods analyzing the same data set?

Thanks a lot.

Phil_Kay · Answer

The multivariate platform is very useful for understanding correlation between a number of variables. It gives you visual and statistical measures of the correlation of each variable with every other variable on a pairwise basis. It can be used as a way to understand where there are relationships between variables.

In your case (from what I understand - correct me if I am wrong) you want to know if X1 has an effect on Y. And if X2 has an effect on Y. Fit Model enables you to answer these question through hypothesis testing. Behind the p-value there is a hypothesis that X has no effect on Y (the "null" hypothesis). The data is then used to tests this hypothesis.

Fit model also provides a model that can tell you what value of Y you can expect for any value of X1 and X2, with associated estimates of uncertainty.

JMPstart · Answer

Phil,

Thanks for your help. Fit model makes sense.

What is "multivariat" method for? Can it be used to answer the question "if Y coorelate with X1, X2 etc"? If it is not appropriate to use multivariate, why?

Phil_Kay · Answer

Hi,

It sounds like you have some uncertainty about some of the concepts like correlation and p-values. It might be a good idea to get some training on basic stats. In particular on regression. There are lots of resources out there to help you, include formal training courses.

To try and help you with your question: you should be able to answer this with the Fit Model platform, as you had started to do.

Y should be in the Y role, of course. Then you can add X1 and X2 in the Construct Model Effects box. The Personality should default to Standard Least Squares, assuming Y is continuous modelling type and has been correctly defined as such in its column properties. Then Run.

The Effect Summary should tell you the relative extent to which X1 and X2 are related to Y. A small p-value indicates an "important" effect. (The correct interepretation of p-values is a bit of a minefield.) People often say that an effect is significant if the p-value is less than 0.05. Although others go for a threshold of 0.01. There is no right answer.

This is by no means an exhaustive answer. You might also want to consider whether X1 or X2 have a curvilinear relationshiop with Y. In which case you would want to add the quadratic terms for X1 and X2. Or even cubic effects and so on. You might also want to consider whether there is an interaction between X1 and X2.

I would start with simply plotting Y vs X1 and Y vs X2 using the Graph Builder and see what that tells you about the relationships. Then go from there.

I hope that helps.

Regards,

Phil