I am trying to conduct a simple 2 way analysis of an experiment; each factor has 3 levels with one replicate each. Both variables are continuous. When running the analysis and looking at the output and parameter estimates I see the following:
(Factor 1 - x) * (Factor 2 - y) where x and y seem to be some averaged/arbitrary value
Can somebody explain how I would use (Factor 1 - x) * (Factor 2 - y) in the regression equation?
Also, what is the best way to determine which levels of the different factors are most significant.
First after fitting your model go to the red triangle and choose save columns> "prediction formula"
This saves the prediction formula for your model to the data table.
Go to your JMP data table and you will notice that a new column has been added at the far right named prediction formula
Double click on the column heading and a dialog box will appear.
Under the column properties pulldown highlight Formula
click edit formula button
go to the red triangle pulldown and chose simplify
That will give you the simplified parameter estimates.
The reason you obtained strange parameter estimates was because you probably chose a 3 level design. You could have accomplished the same thing with a two level design and just added center points which might have been simpler.
I understand now, thanks.
One other question... If I have a data set with 2 factors, but there is only 1 replication/observation (as shwon below), I can't do any interaction analysis because of inssuficient DoF, correct??
Factor A Factor B Response
1 a y1
1 b y2
1 c y3
2 a y4
2 b y5
2 c y6
3 a y7
3 b y8
3 c y9
You should be okay. If the are both 3 level categorical factors the model is pretty saturated but you get the interactions terms delineated. You could also try a stepwise regression to make the model more parsimonious. If one factor is continuous and one is categorical then it appears to me when utilizing the "simulate responses" under the red triangle that you have enough DoF for interactions and the error. Alternatively you could also add an additional row and replicate one of the other combinations.
The 2 factors are quantitative, but can be classified as Nominal.
The reason I asked is because when I run the fit model command with the 2 factors and the cross of the 2 factors as a the model effects, the F test for the model's effects are null. I think it's because each factor has 2 degree of freedom and the interaction has another 4, which makes 8 degrees of freedom. This leaves no degrees of freedom for the error term which is why the F test can't show any results. Isn't that right? If I run the ANOVA without the interaction terms it runs fine. And if I changed one of the factors to a continuous variable it runs fine, but I think in my case they should both be set as nominal.
I was looking online and it seems that as a general rule you cannot properly analyze the interaction between 2 factors with only 1 replicate/combination. I just would like to be sure about this fact.
You are correct. The null is due to the fact that all of your degrees of freedom are used up. That is why I asked you if they could be treated as continuous. Did you try to model using the stepwise model personality?