multivariate regression

[Bradtech519]

Would you use multivariate regression if the two independent variables have a correlation coefficient of 0.88? Or, would you just explore each independent variable separately using linear, exponential, and power regression techniques and pick the solution that gives you the best fit?

 

[CycloWizard]

I wouldn't rely on a correlation coefficient to make this determination. Instead, I would perform a suitable statistical test to determine whether either or both of the variables significantly altered the response. If I had enough data (or data collected appropriately), I would also test the interaction of these two independent variables. I would then use a model which keeps the significant factors and discards the insignificant ones. The model of choice would depend on the distribution of residuals and what I understood about the physics underlying the problem (if any).

 

[Wizlem]

If we are only talking numbers the fact that the two independent variables aren't perfectly correlated means atleast one contains information the other doesn't. If both contained useful information, you should be able to get a better fit using both.

It very much matters what these variables really are. You could easily have correlation between the two that doesn't always occur.

 

[C1]

Depends on what you are trying to do.

Sometimes we use high polynomial fits to be able to accurately describe a physical process. Example fit:

Y= aX + bY + cXY + dX^2 + eY^2 + fX^2Y + gXY^2 + hX^2Y^2 + ........

Order the terms based on their statistical contribution (IVOR or BIVOR process), then drop the terms sequentially until the residual SS shows statistical significant increase. Checkout MRCA Multiple Least Squares Regression. http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0636738

 

[drinkmorejava]

Like the post above, it sort of depends. If it's a physical process that you think you understand, then you're fine. If you're trying to mix random predictors that just happen to be correlated but one doesn't really affect the dependent variable, then you can get funky results.

Generally speaking, normal statistical tests like independent predictors...which is probably why you're asking the question. However, as a whole, your regression model should not be less accurate or have poorer prediction capable because of the correlation.

You're probably fine. My go-to first try would be a quadratic regression including linear interactions.

Also, look up multicollinearity. The wikipedia page will probably reassure you.