How to plot multiple regression 3D plot in python
<p>I am not a scientist, so please assume that I do not know the jargon of experienced programmers, or the intricacies of scientific plotting techniques. Python is the only language I know (beginner+, maybe intermediate). </p>

<p><strong>Task</strong> : 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 <a href="https://stackoverflow.com/questions/7863906/plot-regression-surface">Plot Regression Surface</a> with R).</p>

<p>After a week searching <strong>Stackoverflow</strong> and reading various documentations of <strong>matplotlib</strong>, <strong>seaborn</strong> and <strong>mayavi</strong> I finally found <a href="https://stackoverflow.com/questions/12423601/python-the-simplest-way-to-plot-3d-surface/25586869#25586869">Simplest way to plot 3d surface given 3d points</a> which sounded promising.  So here is my data and code:</p>

<p><strong><em>First try with matplotlib:</em></strong></p>

<pre><code>shape: (80, 3) 
type: &lt;type 'numpy.ndarray'&gt; 
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()
</code></pre>

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

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

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

<p><strong><em>Second try with mayavi:</em></strong></p>

<p>Same data, divided into 3 numpy arrays:</p>

<pre><code>type: &lt;type 'numpy.ndarray'&gt; 
X: [    0   500  1000  1500  2000  2500  3000 ….]

type: &lt;type 'numpy.ndarray'&gt; 
Y: [  0.    0.5   1.    1.5   2.    2.5   3.  ….]

type: &lt;type 'numpy.ndarray'&gt; 
Z: [  5.5272   5.5922   5.6572   5.7222   5.7872   5.8522   5.9172  ….] 
</code></pre>

<p>Code:</p>

<pre><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()
</code></pre>

<p>All I get is this:</p>

<p><a href="https://i.stack.imgur.com/7MNcs.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/7MNcs.png" alt="enter image description here"></a></p>

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

<p>Will be grateful for any input on what I am doing wrong.</p>

<p>EDIT: Posting the final code that worked, in case it helps someone.</p>

<pre><code>'''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()
</code></pre>

<p><a href="https://i.stack.imgur.com/ABq81.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ABq81.png" alt="enter image description here"></a></p>