DOE

sarra

Hi,

I have some questions regarding DOE regression equation.

I don't understand why Minitab converts the regression equation into uncoded units and why is it possible only for hierarchical model? 

Is there a mathematical equation between coefficients of the coded and uncoded units? and how can I interpret the uncoded coefficients?

Thanks,

Mark_Bailey

I cannot speak to the behavior of MINITAB but I can explain the difference between the model parameters when the factors are coded or not.

 

We should at least center our variables when using regression or another linear model technique because it helps reduce the correlation of the estimates. It also provides a meaningful interpretation the intercept: it is the mean response at the origin of the data. Without centering, the intercept often has no real physical meaning. Finally, the scaling aspect means that all the estimates represent half of the change in the response over the entire range of the factor. This way, the estimates a scale invariant and they can be compared, if we are exercising the widest possible range for each factor. (For example, which factors produce the largest effect?) That is not possible without coding. I can make the estimates arbitrarily small or large by a change of scale. (For example, change the units of a dimension from meters to light years and you will see what I mean.)

 

You can remove the coding after you fit the model. This way you can see the unit change in the original scale. Save it as a column formula, open the formula editor, click the red triangle near the keys at the top of the editor and select Simplify. The centering and scaling in the formula involves only constants so they can be converted without loss.

 

NOTE: it is very important that you maintain model hierarchy if you intend to convert between the coded scale and the original scale.

 

Using the original factors and the coded factors give identical model predictions, but we usually expect more of our models.