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How can I generate a non-linear line of best fit with multiple factor/X variables?
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)
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Re: How can I generate a non-linear line of best fit with multiple factor/X variables?
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:
- Select Analyze > Fit Model.
- Select the response columns and click Y, Response.
- Change the default Degree value to 3.
- Select the factor columns.
- Click Macros and select Polynomial to degree.
- (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.)
- Select Keep dialog open in case you decide to add or remove terms in the model after examining the initial regression analysis.
- (Optionally, click the red triangle at the top and select Save to Data Table to avoid setting up this model again.)
- Click Run.
- 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.
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Re: How can I generate a non-linear line of best fit with multiple factor/X variables?
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:
- Select Analyze > Fit Model.
- Select the response columns and click Y, Response.
- Change the default Degree value to 3.
- Select the factor columns.
- Click Macros and select Polynomial to degree.
- (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.)
- Select Keep dialog open in case you decide to add or remove terms in the model after examining the initial regression analysis.
- (Optionally, click the red triangle at the top and select Save to Data Table to avoid setting up this model again.)
- Click Run.
- 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.
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Re: How can I generate a non-linear line of best fit with multiple factor/X variables?
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.
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Re: How can I generate a non-linear line of best fit with multiple factor/X variables?
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.