How can I generate a non-linear line of best fit with multiple factor/X variables?

[#1]

I have three continuous factor variables I am looking to translate into one response variable. A linear best-fit line is not adequate enough for my results. Still looking at multiple regression analysis, but am having a difficult time generating a single line for each regression.

Regression line 1 is three continuous X Variables to one response(also continuous) Y variable.

Regression line 2 is the same continuous X variables to the second(continuous) Y response variable.

I tried using a bivariate analysis, but now I have six different lines of best fit(fit polynomial/cubic). Is there a way to combine those? Only problem is that each factor doesn't evenly contribute to the response variable.

Any help/direction would be greatly appreciated.

In short: 3 factors into two response variables. All variables are continuous. Need two lines of best fit that are not linear(preferably cubic)

[#2 · Accepted solution]

I am not sure what you mean by a 'line' in the context of a response to three factors. It is a surface on a three-dimensional space. A two-dimensional rendering of pseudo-three-dimensional plot could show the surface versus at most two of the factors at a time. You might explore the Surface Profiler toward this end.

On the other hand, you can see a plot of the graph of your model function as a separate line for each factor. This line is a slice in the surface in one dimensional conditioned on the other factor levels. JMP provides a powerful but simple to use plot for this purpose. Try this activity:

1. Select Analyze > Fit Model.
2. Select the response columns and click Y, Response.
3. Change the default Degree value to 3.
4. Select the factor columns.
5. Click Macros and select Polynomial to degree.
6. (Optionally, set the degree to 2, select the factor columns again, click Macros and select Factorial to degree if you want to include terms for two-factor interactions in your model.)
7. Select Keep dialog open in case you decide to add or remove terms in the model after examining the initial regression analysis.
8. (Optionally, click the red triangle at the top and select Save to Data Table to avoid setting up this model again.)
9. Click Run.
10. If the Prediction Profiler is not open (near the bottom of the window) the click the red triangle next to Fit Least Squares at the top and select Factor Profiling > Profiler. (Note the other profilers that you might use with your model.)

Let me know if the Prediction Profiler is the plot that you are looking for.

[#3]

By line I meant formula. Something that could be replicated with many other points, like a regression line.

I came across neural networks, so I went with that, but I will also take a look at your advice also and see where that leads me.

A Neural Network seemed to do the job I wanted.

[#4]

I forgot to mention a few things about the Prediction Profiler.

• This plot is generally available in the fitting platform for most kinds of models, such as Neural, Nonlinear, and so on.
• This plot is always available outside of any fitting platform the the Graph menu > Profiler. Simply save your model as a column formula first. In other words, you do not have to re-fit the model every time you want to profile the model.
• Note that you can generally profile any formula using the second point above.