"Fit Curve" modeling with multiple x variables

[#1]

Hi, I am a beginner with no statistics experience.

My problem is I have a single column of y values, and 6 columns of x values. Y is assumed to be caused by a combination of the 6 x values. 

I am trying to come up with a polynomial, using the x parameters, that model the y. I have successfully done this using least squares regression in JMP (and in python) but the results aren't amazing because my data definitely isn't linearly related. From my understanding, for non-linear fits, the Fit Curve is suitable. However, I'm not sure how to do this with multiple X variables since the "Fit Curve" only accepts one.

Can someone point me in the right direction?

[#2]

The term 'linear' can have many interpretations in statistics. In the Fit Model platform, Standard Least Squares (which is what I'm assuming you have tried?) personality, it's the parameter estimates that are 'linear'...not necessarily the responses. If the responses are not of a 'straight line' nature wrt to the one or more of the x's, then a polynomial expression that is still linear in the parameters may provide an adequate fit. There are two basic techniques modelers use in this instance...transformations of x's (a Box Cox approach here might help inform the type of transformation?) or y's, or estimating higher order terms in the linear polynomial expression (cubic, quartic, etc.). Have you tried these ideas first before resorting to the Fit Curve or other Non Linear modeling capabilities in JMP? The Fit Curve and Non Linear platforms use models where the parameter estimates themselves are non linear wrt to the x variables. Useful platforms for sure...but you may want to exhaust all possible ideas with 'linear' models first if you haven't done so already.

[#3]

 Thank you for the great info.

While I have tried the Standard Least Squares, like you assumed, what I got, after selecting only the 4 most appropriate variables based off of the P>|t| thing, was something with an Adj. RSquare of only 0.18. 

Also like you assumed, I haven't tried the possible ideas with linear models because I wasn't aware of the things you brought up, so thank you very much.

Could you point me in the correct direction for figuring out how to transform my parameters to get the best fit? Like I said, I have no statistics experience, so all I want is any combination of the parameters to best model my y values in any way possible and don't know where to start.

[#4]

Also, let me know if you think it would be more appropriate to start a new post here since my original goal has definitely changed after your very helpful comment.

[#5]

Your phrase "...no statistics experience..." leads me to pause and not recommend any more modeling ideas but to recommend one of two paths:

1. Hire a consultant to do the work with you...especially if this is a one of a kind effort and you don't really want or need to build your competency in statistical methods.

2. Build your basic knowledge of statistical methods. It's kind of like giving you a shiny new car (statistical methods) but you don't know how to drive. And you are asking the community to give you instructions for getting from point A to point B in your shiny new car. So one thought I have for you is to complete the SAS "Statistical Thinking for Industrial Problem Solving" online course. It's free. Upon completion of the course modules you'll build your competency wrt to statistical methods and JMP. Here's a link to the course home page: Statistical Thinking for Industrial Problem Solving  

[#6]

Thank you for your suggestions. I would love to hire a consultant and have already reached out on Fiverr to a few people. Do you know where else would be a good place?

[#7]

I will send you a private message because this type of conversation is not the intended content for this Discussion Forum.

[#8]

Looks like because I am a new user, I do not have access to private messages...