How can I interpolate the following data and get the equation?

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I want to interpolate between three vectors which have 8 rows in each. For eg. X = [1 2 3 4 5 6 7 8], Y = [7 8 9 10 11 12 13 14 ], Z = [15 16 17 18 19 20 21 22] I want to find the equation Z = f(x,y).Can interpolation be used here without neglecting any data or regression is the only option? Because if I try to interpolate using quadratic polynomial there will be 6 variables and I have 8 equations. If I increase the degree to 3 number of variables will be more than 8.