Good evening,
I have a variable Q, dependent on three variables M, K and T, as displayed in the attached image. I conducted numerical simulations to evaluate the relationship between Q and 1 variable at a time while keeping the other two constant. In total I have 9 sets of data as in the attached image.
The thing Q is not linearly dependent on either of them. Is there any way to find an equation of q in terms of all three, as in Q = M + k +t sort. Which software would be best.
Thank you
Using R Language
q = c(2,2.5,2.7,2.5,2.6,2.7,2.5,3,3.5)
m = c(0.2,0.6,1,0.6,0.6,0.6,0.6,0.6,0.6)
k = c(325,325,325,325,335,345,325,325,325)
t = c(15,15,15,15,15,15,15,20,25)
df = data.frame(q,m,k,t)
## adjust a multiple linear model
fit = lm(q~., data = df)
fit$coefficients
# equation
# q = -4.0138 + m * 0.875 + k* 0.01333 + t * 0.1066
# (Intercept) m k t
#-4.01388889 0.87500000 0.01333333 0.10666667
summary(fit)$r.squared
# R2 = 0.9788557
Elpidio Inacio Fernandes Filho thank you very much for the reply. If however i donnot have such linear arrangement as in this dataset (R2 is not close to 1), do you recommend any other method ?
They is performed in a similar way tan the single. Using each variable.
You asked about interpolation but you did not give any information about spatial dependence so it appears you are not really interested in interpolation. However you might want to try multivariate regression but it will likely involve some experimentation to determine the right choices for the form of the regression model, i.e. should you use polynomial functions of M, K, T in the regression equation or something else (perhaps logarithmic or exponential.
You mention having used simulation but to do that you need some information on functional dependence and/or it is not clear by what you mean by "simulation"
I suggest you start with original data, assuming you have some then make scatter plots of Q vs M, Q vs K, M vs T.
See the following link
https://maitra.public.iastate.edu/stat501/lectures/Visualization.pdf
and especially the free software package ggobi
It is very good because it is interactive and also because it can be use in connection with R (the suggestion by Elipdio is not complete, there are many "packages" accessible from within the R software, all are open source, there are several multiple regression choices and good documentation
q = 2,2.5,2.7,2.5,2.6,2.7,2.5,3,3.5
m = 0.2,0.6,1,0.6,0.6,0.6,0.6,0.6,0.6
Hope you got the clue...Thank you
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