ANCOVA: Interpret the JMP ANCOVA result. (4 possible combination)

[#1]

Hello all.

I am having problem with interpretating the ANCOVA in JMP.

Problem 1.

Can I use IV as "continuous variable" & "DV as continuous, CV as categorical" ?

Since I had read many reference that saying "ANCOVA need IV-categorical, DV-continuous, CV-continuous".

It is very confusing, since if IV is categorical, IV and DV relationship can not be defined as linear regression... they are just ANOVA...

isn't it??

Problem 2.

There are 4 possible JMP output in ANCOVA

1- slope different, intercept different

2- slope same, intercept same

3- slope different, intercept same

4- slope same, intercept different

How can I interpret 1 and 3 cases?

There seems to be the other approach when this situation comes in,

but it is too complicated.

Please help me.

[#2]

Thank you and it is interesting.

However, what is the point of pooling?

pooled line and one of the existing line (e.g.: A460 1) are subjected to be compared?

I don't think I need that.

The final conclusion I want to draw is whether the lines are all same or not..

Given your jmp file, 

The problem rises when interaction is significant and intercept is not. (or vice versa)

[#3]

I wonder whether using the Fit Curve platform might be an option.  This platform supports the comparison of parameters; I've only ever used it for nonlinear relationships but you can use it with a linear model.  Here you can do an equivalence test in the form of Analysis of Means (ANOM) for each term in the model.

Here is a comparison of the slopes for the data supplied by @Byron_JMP 

Here is the link in JMP's online help:

parameter comparison 

[#4]

One other suggestion is to add the covariate term FIRST in the model and then assess the significance of it using sequential tests (type1).  Use partial tests (type 3) to assess the remainder of the model terms.