estimates in multipule regression

[#1]

Hello,

I have an issue in JMP pro10.

I am performing a multiple regression with 3 continuous variables (x1,x2,x3) and an interaction between x2*x3

The estimates that I get for the interaction are usually in the following form:

(x1 - "number")*(x2-"number"), I do not understand this report method, but the estimates worked well for predicting new values.

I wanted to report these estimates without the "number" subtracted. I went to r and performed the same analysis and I got the exact same R2 so I know that It was the same analysis. The estimates that I got were different but it work exactly as the function JMP gave me, only without the "number".

I searched here and found a post ( Need help understanding interaction variable) that explain how to get the estimates without the "numbers" subtracted in JMP. After using the suggestion, the estimates were exactly the same as in r.

Now things start to be messy:

The t values (and P values) are not exactly the same between the two outputs that I have (JMP and r).

x1   and   x2*x3  -> has exactly the same t values (and P values)

x2, x3,               -> as a standalone are very different between the softwares.

Can anyone tell me what may be the reason for these differences? or perhaps something about JMP model assumption that may influence the t values?

Thanks

[#2]

@MRB3855, I am amazed at this coincidence. Very basic question for you, very difficult for me: If I add the terms you suggest, I will have an approximation of the Arrhenius equation? Also, what other information in this presentation is too incomplete to allow direct use by a novice model fitter?

[#3]

Hi @Ressel : To follow up, here is my take (in no particular order):

1. Keep in mind that the Arrhenius equation (page 12)  shows the relationship between the slope and the temperature. So, k is the slope at a given temperature. As you can see on page 7, the slope (k) gets steeper with increasing temperature.

2. Generally speaking (and speaking as a statistician), it's rare that you would not include the lower order terms when there are interactions which include those terms. However, this is one of those rare cases where you would not include those terms. That is because they are using a Taylor series (actually a Maclaurin series, which is a special case of a Taylor series) approximation for k; they did not have to do this; in principle, they could have used the first equation below (from page 16) directly. But that is a nonlinear model and would be more cumbersome. The red circle below really should encompass the entire exponential portion of expression for k (as shown by my green circle).  The term in brackets is then the Taylor series approximation for k/A (it actually goes on infinitely, but the idea is that the first few terms will get you close enough). Using this approximation they can use the all the benefits of a linear model. If you look carefully at the first equation below, it is just the equation of a straight line, with the slope, k, replaced by the Arrhenius equation.

3. On page 17 they recommend centering Arh(T); this is a good idea for interpretation of the coefficient A; i.e., create a variable, Arh(T) - Arh(T0), to use in your model (rather than Arh(T) directly).

4. There is more to talk through perhaps, but I'll leave it here for now. The link below may be of some help (in particular, see the last example in the Example section).

https://en.wikipedia.org/wiki/Taylor_series

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[#4]

Thanks Julian for the immensely detailed and helpful answer. I consider the problem solved now.

Also thanks mpb for the helpful tip