Given the following data points
| X | Y | Z |
|---|---|---|
| 18.23 | 3 | 80 |
| 42.2 | 5.5 | 600 |
| 377.30 | 52.04 | 900 |
| 6835.86 | 646.91 | 17 000 |
| X | Y | Z |
|---|---|---|
| 250 | 20 | ? |
Can I find the function of X and Y that best predicts the value of Z?
In my (basic) understanding, a multivariate regression will give me the equation of a plane, which is not super precise.
How can I get the equivalent of a polynomial function as the fitting function? What tool can I use?
The points are not close to a plane. If you try to fit a plane the fitting will be bad especially for the low values of z ( if the criteria of fitting is Least Mean Square Error ) . See the next result :
Since they are only four points one can have an exact fit with any equation on the form
y=a * f1(x) + b * f2(x) + c * f3(x) + d * f4(x)
where f1, f2, f3, f4 are arbitrary undependant functions. Thus they are infinity many solutions.
Among so many solutions why not a very simple one ? For example :
The result is exact : Perfect fittig.