Help interpreting parameter estimates, prediction equation, and std error

[#1]

In the Fit Least Squares analysis, My model has a categorical variable, "Section" with three values "1", "2", and "3," and one continuous variable, "Cycles."  I have three questions.

1. Why doesn't the Parameter Estimates table represent the model? It gives me no information about Section "3".
2. Can I change the options in JMP so the analysis output excludes the intercept coefficient and just returns Section "1", "2", and "3" coefficients as 0.655, 0.789, and 0.804?
3. How do I interpret the total standard error for a given Section? Do I just stick with the Std Error in the LSM table, or do I add up the Std Error of the parameter estimates? i.e  Std Error (Intercept) + Std Error (Section[#]) + St Error (Cycles)?

[#2]

I'll provide a few answers. 

1.  JMP will leave out one value of a nominal variable in a regression model and report the coefficients for all the others - each coefficient is interpreted as the effect of that category relative to the average of all categories.  This is necessary, since the model would be over-identified if all categories were used as factors.  You can see the coefficient for all categories, by clicking on "Expanded estimates" after running the model.  In the case where there are 2 categories, say 0 and 1, JMP will give a coefficient for category 0, and the difference in the response variable between the two categories will be 2x that coefficient (expanded estimates will show category 1 has a coefficient with the same absolute value, but the opposite sign).

2.  To exclude the intercept, just check the box "no intercept" when creating the Fit Model.

3.  I'm not exactly sure what you are asking here.  But if you want the overall standard error for the model, use the Standard Error reported in the summary of the fit (not any individual coefficient, but the standard error of the residuals from the model).

[#3 · Accepted solution]

Thanks for the reply.

1. Yes, the expanded estimate is what I was looking for.
2. Setting the overall model to intercept at zero is not what I meant. Rather, I wanted the parameter estimates for Section[#] to already include the intercept (not the difference from the intercept). But I think this goes against statistical conventions and I can compute what I want easily enough. 
3. I was trying to find the standard error for all data in a given section. I realize now this is not the standard error of the parameter estimates. Neither is it the standard error in the LSM plot. The LSM plot standard error is calculated with a pooled standard deviation because the LSM plot assumes equal variance among all factor levels. If I want the standard error for one section, I have to compute it separately, which I found easy enough to do with the Tabulate tool.

[#4]

I don't recommend doing this often, but to "see" the model without the intercept you could always fit the model with the section as a "by" variable (and remove section from the model, of course). You will get three models, one for each section. The intercept for each model will be the intercept combined with the parameter estimate for the respective section.

This approach might allow you to get at the "standard error" you were looking for also. 

I usually only recommend this approach in order to understand the single overall model that you have already fit. One model would be preferable over three.