Can i surface plot three vectors and fit a curve to get an equation of that surface?

The following code gives me a 3D line plots as shown, i want to fit a 3D surface but whenever i am trying to use commands like patch, meshgrid, surf - Matlab gives an error saying "z must be a matrix and not a vector".

In other words, i intend to do 2 things,

1. Surface plot the following data
2. Fit an equation to get a values for intermediate values, similar to interpolation

Even if you could guide me on one of the above, please consider answering this.

I have attached the code and image of plot below

x =[400;500;600;700;800;900;1000];
y1 = [60;60;60;60;60;60;60];
z1 = [3.2;4.1;5;5.8;6.6;7.5;8.16];
plot3(x,y1,z1);
hold on

y2 = [100;100;100;100;100;100;100];
z2 = [2.7;3.46;4.15;4.8;5.55;6.2;6.9];
plot3(x,y2,z2);

y3 = [125;125;125;125;125;125;125];
z3 = [2.5;3.17;3.81;4.4;5.1;5.7;6.2];
plot3(x,y3,z3);

y4 = [150;150;150;150;150;150;150];
z4 = [2.2;2.8;3.4;4.0;4.6;5.1;5.6];
plot3(x,y4,z4);

xlabel('x');
ylabel('y');
zlabel('z');
grid on