Is there a way to make a plane of best fit using matplotlib? I'm trying to get a smooth curved plane or even just a flat one, but I'm unsure on how to do so.
My points are arranged as shown in the following image:
They are quite smooth, except for a few exceptions, which are mostly clear.
My current code is:
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
from sklearn import linear_model
plt.style.use('seaborn-poster')
x = np.array([12.5, 10, 9.5, 7.5, 6])
y = np.array([30, 45, 50, 55, 60, 65])
z = np.array([
[62.13, 55.41, 54.49, 46.46, 42.13],
[67.11, 59.43, 56.39, 52.64, 41.89],
[82.89, 61.13, 57.30, 50.75, 43.02],
[73.31, 60.57, 57.17, 52.64, 41.73],
[78.11, 62.92, 63.40, 58.08, 48.69],
[83.96, 65.19, 60.22, 53.57, 44.22]
])
X, Y = np.meshgrid(x, y)
Z = z
x1, y1, z1 = X.flatten(), Y.flatten(), Z.flatten()
X_data = np.array([x1, y1]).reshape((-1, 2))
Y_data = z1
reg = linear_model.LinearRegression().fit(X_data, Y_data)
a1, a2, c = float(reg.coef_[0]), float(reg.coef_[1]), float(reg.intercept_)
fig = plt.figure(figsize = (9,9))
ax = plt.axes(projection='3d')
ax.grid()
ax.plot_surface(X, Y, z)
ax.scatter(X, Y, z, c = 'r', s = 50)
ax.set_title('Figure 1.21 - Plot of Final results')
ax.set_xlabel('Radius of Ball (mm)', labelpad=20)
ax.set_ylabel('Height from which ball was dropped (cm)', labelpad=20)
ax.set_zlabel('Diameter of ripple (mm)', labelpad=20)
plt.show()
I have the a1, a2 and c values using linear regression but how do I plot them? Is linear regression going to give the right sort of result for this graph? I'm quite new to matplotlib, so sorry if this seems obvious.
