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## How to fit a model with dependent factors?

Hi I have a DOE with 3 factors: Chamber pressure, Flow rate, and voltage. Two of these factors are dependent on each other (Pressure and flow rate). Meaning i am changing the flow rate for specific pressures and not mixing them with different levels. When i fit the model with the 3 factors i don't see any correlation because i essentially have 2 factors. When i remove one of the dependent factors i see a correlation. Can someone explain why this occurs?

Thanks,

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## Re: How to fit a model with dependent factors?

Based on the information available the data alone, it is impossible to simultaneously estimate the two effects. For example, when X1 = 10 and X2 = 5, Y = 20. When X1 = 20 and X2 = 10, Y = 40. What is the effect of X1? What is the effect of X2? You may arbitrarily assign the effect to either X1 or X2 but this data is insufficient to determine which it is. Another way to look at it is that there are an infinity of solutions that solve this problem.

You should have noticed a Singularities Details report at the top of the Fit Least Squares window warning you about this problem. Your effects are perfectly correlated, or confounded. They are inseparable.

Is this confounding a problem? It is for regression. But do you need both variables in the model? It sounds like you use flow rate to achieve pressure. So it seems to me that pressure is the factor and flow rate is not a factor but a way to achieve a factor level. It would be like including the weight of a chemical dissolved in water and the concentration of the chemical in the same model. The concentration is the factor. The weight is the way to achieve a specified concentration.

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