it is a^x3+b^y3...sorry for the typing error (not a^x3+b^x3).
cheers,
Martin
Hi All,
I posted this question to the pre-university problem a few days ago, but it seems nobody can answer, so I will try my luck here.
I want to approximate a surface with a cubic regression in the following form. (Where X is the temperature, Y time and and z the energy requirement: Thus f(x,y)=z.)
a⋅x^3+b⋅x^3+c⋅x^2⋅y^2+d⋅x^2⋅y+e⋅x⋅y^2+f⋅x^2+g⋅ y^2+ h⋅x⋅y+i⋅x+j⋅y+k
However I am not sure if I wrote correctly the cubic equation???
If somebody could tell me wherever it is correct or not. And if not, what is wrong :-)
a,b,c,d,...etc. are the coefficients.
By the way, what is the general form of such two variables dependent quadratic or cubic equations?
Thanks a lot in advance.
Cheers,
Martin
Write it as:
The following Mathematica code first generates a list {{x_1,y_1,z_1},. . .{x_n,y_n,z_n}} for the function then fits the data points to u(x,y) then superimposes the plots to obtain a quick visual indication of how well the fit was determined.
Code:f[x_,y_]=Sin[x y]; mytable = Flatten[Table[{x, y, f[x, y]}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], 1]; myequation = a + b*x + c*y + d*x^2 + e*y^2 + f*x*y + g*x^2*y + h*y^2*x + i*y^3 + j*x^3; myconstants = FindFit[mytable, myequation, {a, b, c, d, e, f, g, h, i, j}, {x, y}] pic2 = Plot3D[myequation /. myconstants, {x, -1, 1}, {y, -1, 1}, PlotStyle -> Blue] Show[{pic1, pic2}]