# [MiniTab] Correlation/interaction among Dependant Variables

#### Lawrence

##### New Member
Dear all,

I have been recently analyzing a DOE which has 4 factors (Independent variables) and 12 Responses (Dependent variables).

My task is to dig out whether there is any interaction between these 12 DVs.
Can I use MANOVA in Minitab to achieve this goal?

Thanks in advance!

Cheers,
Lawrence

#### Miner

##### TS Contributor
What do you mean specifically by interaction? I ask because factors (IVs) can interact, but response do not interact unless they in turn become factors for other responses.

You could have responses that correlate with each other. Is that what you mean?

#### Lawrence

##### New Member
What do you mean specifically by interaction? I ask because factors (IVs) can interact, but response do not interact unless they in turn become factors for other responses.

You could have responses that correlate with each other. Is that what you mean?

Hi Miner,

Yes, I mean the correlation that the responses have with each other.

How do I get a equation for this correlation, like the one we get when performing regresision for IDVs?

IE. Response 1 = Constant + Coeff*Response 2 + Coeff*Response 3 + Coeff*Response 4...
Response 2 = Constant + Coeff*Response 1 + Coeff*Response 3 + Coeff*Response 4...
Response 3 = Constant + Coeff*Response 1 + Coeff*Response 2 + Coeff*Response 4...

I read from wiki that MANOVA helps to answer:

Do changes in the independent variable(s) have significant effects on the dependent variables?
What are the interactions among the dependent variables?
And among the independent variables?

Thanks so much!

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#### GretaGarbo

##### Human
I was reading the text wrong and believed that the 12 responses were 12 observations. How many observations did you have?

Does the DOE here means design of experiments? Was it a "usual" design like a two-level factorial?

Lawrence is using the words 'interaction' and 'correlation' in a little bit different way than what is usual in statistics.

(What is "IDVs"?)

#### Lawrence

##### New Member
I was reading the text wrong and believed that the 12 responses were 12 observations. How many observations did you have?

Does the DOE here means design of experiments? Was it a "usual" design like a two-level factorial?

Lawrence is using the words 'interaction' and 'correlation' in a little bit different way than what is usual in statistics.

(What is "IDVs"?)
Hi GretaGarbo,

My apologies to have those words incorrectly used. Please allow me to clarify the confusion.

You are right that I am working on a Design of Experiment. It is a 4-factors, 12 responses, 2 level full factorial design.

From my understanding, the 4-factors here are considered as "Independent variables (IDVs)" while the 12 responses are the items to be measured, and are considered as "Dependent Variables (DVs)".

As far as I know, ANOVA is capable of determining the influence of the 4 factors on the 12 responses, which has been done already.

It is believed that apart from the influence mentioned, the 12 responses also affect or at least change with each other.

What I am desperately trying to develop is a set of equations which capture the relationship between these 12 responses.

I don't know whether it is actually achievable or not. However I keep reading articles on Internet that say MANOVA or Multivariate regression can do it, although they don't demonstrate the procedure of how it is done.

It must quite frustrating to discuss with a statistic amateur like me. I appreciate your patience and input.

#### GretaGarbo

##### Human
The usual thing is to estimate the multivariate model:

y1 y2 .... y12 = X*B + E

where y1 y2 .... y12 set up a matrix of observations vectors for the 12 response variables, where X is the design matrix and B is the matrix of the estimates for all the 12 response variables and the E is a matrix of disturbance terms. When that model have been estimated then most of the variation has been withdrawn from the matrix of y-variables. What remains is the E-matrix. you could do a multivariate investigation on the E-matrix, like principal components, if you like. A simple investigation is to simply estimate the correlation matrix for E. If that is close to zero, then there is no idea to continue with something more difficult.

An other possibility could be to use a structural equation model. But I guess that that would be to complicated for you at the moment.

#### Lawrence

##### New Member
The usual thing is to estimate the multivariate model:

y1 y2 .... y12 = X*B + E

where y1 y2 .... y12 set up a matrix of observations vectors for the 12 response variables, where X is the design matrix and B is the matrix of the estimates for all the 12 response variables and the E is a matrix of disturbance terms. When that model have been estimated then most of the variation has been withdrawn from the matrix of y-variables. What remains is the E-matrix. you could do a multivariate investigation on the E-matrix, like principal components, if you like. A simple investigation is to simply estimate the correlation matrix for E. If that is close to zero, then there is no idea to continue with something more difficult.

An other possibility could be to use a structural equation model. But I guess that that would be to complicated for you at the moment.

so it can be done by hand calculation only? Any chance that I can do it with Minitab?

Thanks!