How to plot multiple regression 3D plot

Question

Task : Plot the results of a multiple regression (z = f(x, y) ) as a two dimensional plane on a 3D graph (as I can using OSX’s graphing utility, for example, or as implemented here Plot Regression Surface with R).

After a week searching Stackoverflow and reading various documentations of matplotlib, seaborn and mayavi I finally found Simplest way to plot 3d surface given 3d points which sounded promising. So here is my data and code:

First try with matplotlib:

shape: (80, 3) 
type: <type 'numpy.ndarray'> 
zmul: 

[[  0.00000000e+00   0.00000000e+00   5.52720000e+00]
 [  5.00000000e+02   5.00000000e-01   5.59220000e+00]
 [  1.00000000e+03   1.00000000e+00   5.65720000e+00]
 [  1.50000000e+03   1.50000000e+00   5.72220000e+00]
 [  2.00000000e+03   2.00000000e+00   5.78720000e+00]
 [  2.50000000e+03   2.50000000e+00   5.85220000e+00]
 ……]

import matplotlib
from matplotlib.ticker import MaxNLocator
from matplotlib import cm

from numpy.random import randn
from scipy import array, newaxis
Xs = zmul[:,0]
Ys = zmul[:,1]
Zs = zmul[:,2]


surf = ax.plot_trisurf(Xs, Ys, Zs, cmap=cm.jet, linewidth=0)
fig.colorbar(surf)

ax.xaxis.set_major_locator(MaxNLocator(5))
ax.yaxis.set_major_locator(MaxNLocator(6))
ax.zaxis.set_major_locator(MaxNLocator(5))

fig.tight_layout()

plt.show()

All I get is an empty 3D coordinate frame with the following error message:

RuntimeError: Error in qhull Delaunay triangulation calculation: singular input data (exitcode=2); use python verbose option (-v) to see original qhull error.

I tried to see if I could play around with the plotting parameters and checked this site http://www.qhull.org/html/qh-impre.htm#delaunay, but I really cannot make sense of what I am supposed to do.

Second try with mayavi:

Same data, divided into 3 numpy arrays:

type: <type 'numpy.ndarray'> 
X: [    0   500  1000  1500  2000  2500  3000 ….]

type: <type 'numpy.ndarray'> 
Y: [  0.    0.5   1.    1.5   2.    2.5   3.  ….]

type: <type 'numpy.ndarray'> 
Z: [  5.5272   5.5922   5.6572   5.7222   5.7872   5.8522   5.9172  ….]

Code:

from mayavi import mlab
def multiple3_triple(tpl_lst):

X = xs
Y = ys
Z = zs


# Define the points in 3D space
# including color code based on Z coordinate.
pts = mlab.points3d(X, Y, Z, Z)

# Triangulate based on X, Y with Delaunay 2D algorithm.
# Save resulting triangulation.
mesh = mlab.pipeline.delaunay2d(pts)

# Remove the point representation from the plot
pts.remove()

# Draw a surface based on the triangulation
surf = mlab.pipeline.surface(mesh)

# Simple plot.
mlab.xlabel("x")
mlab.ylabel("y")
mlab.zlabel("z")
mlab.show()

All I get is this:

If this matters, I am using the 64 bit version of Enthought's Canopy on OSX 10.9.3

Will be grateful for any input on what I am doing wrong.

EDIT: Posting the final code that worked, in case it helps someone.

'''After the usual imports'''
def multiple3(tpl_lst):
    mul = []
    for tpl in tpl_lst:
        calc = (.0001*tpl[0]) + (.017*tpl[1])+ 6.166
        mul.append(calc)
    return mul

fig = plt.figure()
ax = fig.gca(projection='3d')
'''some skipped code for the scatterplot'''
X = np.arange(0, 40000, 500)
Y = np.arange(0, 40, .5)
X, Y = np.meshgrid(X, Y)
Z = multiple3(zip(X,Y))

surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1,cmap=cm.autumn,
                       linewidth=0, antialiased=False, alpha =.1)
ax.set_zlim(1.01, 11.01)
ax.set_xlabel(' x = IPP')
ax.set_ylabel('y = UNRP20')
ax.set_zlabel('z = DI')

ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()

Your data are not z=f(x,y) for a 2D grid of xy values, but just along a line y=x. And you don't need Mayavi which is to plot data = f(x,y,z). For z=f(x,y) data Matplotlib is just fine. — roadrunner66, Mar 09 '16 at 06:42
Can you please explain how my data is structurally different from the data that is on the linked page "Python the simplest way to plot 3d surface" ? I tried to replicate the structure and type of that data... — user2738815, Mar 09 '16 at 09:47
for matplotlib, you can base off the [surface example](http://matplotlib.org/examples/mplot3d/surface3d_demo.html) (you're missing `plt.meshgrid`) — Felipe Lema, Mar 09 '16 at 19:14
@FelipeLema Thanks much, your suggestion ended up working for me. Can you post it as an answer so I can upvote and accept it? — user2738815, Mar 10 '16 at 08:20

score 3 · Accepted Answer · answered Mar 10 '16 at 12:36

for matplotlib, you can base off the surface example (you're missing plt.meshgrid):

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.gca(projection='3d')
X = np.arange(-5, 5, 0.25)
Y = np.arange(-5, 5, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,
                       linewidth=0, antialiased=False)
ax.set_zlim(-1.01, 1.01)

ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))

fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()

How to plot multiple regression 3D plot

1 Answers1