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## Finding Correlation between responses

Hi,

Is there a method for us to determine the correlation between two responses?Lets say I have 5 factors A,B, C, D & E. The response that I have is X,Y, Z. What is the best analysis to show that X & Y are correlated and only X response is actually dependent towards the 5 factors while Y is actually a response of the X.

Rgrds

Irfan

1 ACCEPTED SOLUTION

Accepted Solutions
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## Re: Finding Correlation between responses

It seems that a simple approach would be simple linear regression of Y on X using the Bivariate platform. If you establish a high correlation, then Y is essentially redundant. This analysis does not determine if X or Y is the response. Either one could be the response. So the decision, without additional information, is arbitrary.

A more complex approach would be partial least squares of (X,Y,Z) on (A,B,C,D,E). PLS can tell you about the correlation among the factors, among the predictors, and between the factors and the predictors. PLS can indicate if X and Y are correlated and if they are related to the factors the same way.

Learn it once, use it forever!
6 REPLIES 6
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## Re: Finding Correlation between responses

It seems that a simple approach would be simple linear regression of Y on X using the Bivariate platform. If you establish a high correlation, then Y is essentially redundant. This analysis does not determine if X or Y is the response. Either one could be the response. So the decision, without additional information, is arbitrary.

A more complex approach would be partial least squares of (X,Y,Z) on (A,B,C,D,E). PLS can tell you about the correlation among the factors, among the predictors, and between the factors and the predictors. PLS can indicate if X and Y are correlated and if they are related to the factors the same way.

Learn it once, use it forever!
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## Re: Finding Correlation between responses

Hi Mark,

Do you have any example to show how does the PLS shows the correlation between the predictors? As you mentioned in your earlier statement without additional information the knowledge of which response is the actual response, what additional information is required to determine this?

Rgrds

Irfan

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## Re: Finding Correlation between responses

@albiruni81 I've been following this thread from the sidelines. My colleague @markbailey has provided sound advice.

For an example of PLS and correlation among predictors AND responses I suggest taking a look at the Baltic.jmp data table which is in the JMP Sample Data Directory. Just run the embedded script in the data table to perform the analysis. There are several visualizations within the platform report that provide insight wrt to correlation among the x's and y's. There is also a narrative for this particular data table in the JMP documentation. You may also want to take a look at an On Demand Advanced Mastering JMP event I recorded:

https://www.jmp.com/en_us/events/ondemand/mastering-jmp/partial-least-squares.html

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## Re: Finding Correlation between responses

Thanks Peter/Mark

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## Re: Finding Correlation between responses

hello,

1. The cross correlation between the observed series is of little value . You should use single pre-whitening to aid the initial identification. Make sure you account for anomalies in the individual x's before you form the arima filter

2. use pre-whitening

3. make each variable stationary and use the filter for each of the x's separaetely to estimate the ccf

4. no need to use Granger here ,, you are trying to identify an initial model

5. absolutely no detrending is needed to create the arima filters unless they are needed in concert with the arima model

regards
jayesh
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## Re: Finding Correlation between responses Hi,

If i have a correlation as shown above whereby the F is a response for D & E but the factor D is actually a response of A & B. How do i construct a DOE experiment. This is what i wanted to ask, is it possible for the DOE table to generate this kind of relationship

Rgrds

Irfan