# Multi-adaptive Regression Splines (MARS) equation interpretation

I was curious about certain aspects of multi-adaptive regression splines (MARS or earth in R). Taking the equation of MARS from the wiki page:

  ozone = 5.2 +
+ 0.93max(0,temp - 58)
- 0.64max(0,temp - 68)
- 0.046max(0,234-ibt)
- 0.016max(0,wind-7)max(0,200-vis)


My questions are:

1) How to interpret the above equation? If I understand it correctly, for the following value of temp = 52, ibt = 230, wind = 8 and vis = 190, the above equation will become:

      ozone = 5.2 +
+ 0.93max(0,52 - 58)
- 0.64max(0,52- 68)
- 0.046max(0,234- 230)
- 0.016max(0,8-7)max(0,200-190)

ozone = 5.2 +
+ 0.93max(0,-6)
- 0.64max(0,-16)
- 0.046max(0,4)
- 0.016max(0,1)max(0,10)

ozone = 5.2 +
+ 0
- 0
- 0.184
- 0.16


Is this correct?

2) Before running earth (MARS), do the predictor variables have to uncorrelated? What is the way to go about it: remove the correlated predictor variables and then run MARS or run MARS using all predictors and somehow MARS deal with the correlation

3) In R, for earth equation, how do I take out the final equation in step 1 for my model

4) Lets say I run two MARS model: first model predictor x1, x2 and x3 are retained in the final model and in second model x1 and x2 are retained in the final model. Is there any way I can combine the two MARS equation to have a single equation presumably where parameters of x1 and x2 are average of the two models and x3 on its own.

EDIT

To elaborate on (4), let's say I collect some data and and develop a MARS model

 ozone1 = 5.2 + 0.93max(0,temp - 58) - 0.64max(0,temp - 68)- 0.046max(0,234-ibt)- 0.016max(0,wind-7)max(0,200-vis)


I go back and collect another set of data and develop a second model:

  ozone2 = 4.6 + 0.89max(0,temp - 58) - 0.033max(0,234-ibt)- 0.016max(0,wind-7)max(0,200-vis)


Can I combine the two equation in a single equation something like this:

   ozone.fin = (5.2 + 4.6)/2 + ((0.93 + 0.89)/2)max(0,temp - 58) - 0.64max(0,temp - 68) - (0.046+0.033/2)max(0,234-ibt) - 0.016max(0,wind-7)max(0,200-vis)


Thaks

• Why the downvote? Jan 15, 2018 at 10:50