how to generate an interaction plot based on parameter estimate output?

[#1]

 I am analyzing a set of data about graph performance. I am comparing surface graphs with non surface graphs. In this analysis I have two tasks, A and B. I'm measuring the absloute difference (=participant's answer-correct answer). 

ABSDifference is ranging from 0 to 100. Its distribution is like a half normal distribution. 

To analyze this dataset, I used Fit Model, ABS differnce as Y by Graph and Taskusing full factorial. Personality is standard least square. 

I got the following results: 

Analysis of Variance:

Source        DF             Sum of Squares              Mean Square                    F Ratio
Model          3                      4367.12                         1455.71                            4.1790
Error           2204                767740.17                         348.34                          Prob > F
C. Total       2207                772107.29                                                              0.0058

Parameter Estimates

Term                                   Estimate                Std Error           t Ratio               Prob>|t|
Intercept                             21.439143             0.48646              44.07              <.0001
SUR[1]                               0.3552453              0.48646               0.73                0.4653
Task[A]                               0.4607602             0.48646               0.95                0.3437
SUR[1]*Task[A]                   -1.052311              0.48646               -2.16               0.0306

Indicator Function Parameterization

Term                                       Estimate         Std Error     DFDen     t Ratio       Prob>|t|
Intercept                                19.570827       0.561716     2204.0    34.84        <.0001
SUR[1]                                   2.8151123       1.123432    2204.0     2.51          0.0123
Task[A]                                 3.0261421        0.972921    2204.0     3.11           0.0019
SUR[1]*Task[A]                    -4.209243         1.945841     2204.0     -2.16         0.0306

Least Squares Means Table

Level           Least Sq Mean            Std Error
1,A              21.202838                1.3759176
1,B               22.385939               0.9729207
0,A               22.596969               0.7943864
0,B                19.570827               0.5617160

The interaction profiles that jmp gives me is based on Least Squares Means Table. 

Now my questions are:

1- I'm confused between Parameter estimates and the indicator function parameterization. Which table should I report? 

2- why the least squares means table is based on the intercept of indicator function parameterization and not the parameter estimates? 

3- How can I get interaction plot basd on on the data in the Parameter Estimates?

[#2]

1. You should report the estimates that you want or that are expected by convention. See Help > Books > Fitting Linear Models, then search for 'indicator parametrization estimates' for a complete description. Why did you ask JMP for these parameter estimates?

2. The LS Means is based on the parameter estimates, so when you asked for the indicator parameter estimates, the values changed.

3. Click the red triangle at the top and select Factor Profiling. The sub-menu will show you various profilers, including the interaction plot.

[#3]

Hello Mark, 

Thank you very much for your quick reply. I am so happy to see how supportive this community is. I am new to JMP and data analysis. So, please bear with me.  

1- My hypothesis is that performance of surface graph improves when we move from task B to task A comparing other graphs. Both tables are showing a significant improvement. \

2- when I use LS means, in the parameter etsimates table I get the 21.43 as the intercept. While in the LS means table I have 19.57 as the LSM for the other graphs in task B. This value is the same as the intercept in Indicator Function Parameterization. Whether I ask for the indicator paramter estimates or not the values in the LSM table are the same and do not match the intercept in the parameter estimates table. 

3- The interaction profile that is given is also based the values of LSM table that matches the values of Indicator function parameterization table. I want the interaction polt that matches the values of parameter estimates table.

[#4]

You do not seem to need or want the indicator parametrization estimates, so do not ask for them. It is causing unnecessary confusion.

The LSMeans are the predicted mean response for each level of the categorical factor while holding the other factors to a neutral value. None of the LSMeans are the intercept alone unless the parameter estimate for that level is eactly zero.

The Interaction Plot is based on the parameter estimates.