具有 2 个特征的 Scikitlearn 线性回归

Question

I am new to scikit learn and trying to fit a simple linear regression model. I have a matrix X which contains 2 columns, c1 and c1^2, and I have the corresponding y values. I tried to fit a simple OLS model using scikit learn but am getting strange plot in the end. Any ideas on what I am doing wrong?

X = np.array([[ -0.016746535778021,   0.280446460564527],
  [-0.014577470749242,   0.212502653445002],
   [0.034515758657299,   1.191337595688933],
  [-0.047010075743201,   2.209947221381472],
   [0.036975119046363,   1.367159428492700],
  [-0.040686110015367,   1.655359548182586],
  [-0.004472010975766,   0.019998882167376],
  [0.026533634894789 ,  0.704033780729957],
  [-0.042797683100180,   1.831641678743394],
   [0.025374099383528,   0.643844919525139],
  [-0.031109553977308,   0.967804348667025],
   [0.027311768635213,   0.745932705983427],
  [-0.003263862013657,   0.010652795244191],
  [-0.001818276487116,   0.003306129383598],
  [-0.040719662402516,   1.658090906174888],
  [-0.050013243645495,   2.501324539943689],
  [-0.017411771548016,   0.303169788440313],
   [0.003588193696644,   0.012875134004637],
   [0.007085480261971,   0.050204030542776,],
   [0.046282369018539,   2.142057681968212],
   [0.014612289091657,   0.213518992498145]])*1e3

y = np.array([4.1702,
    4.0673,
   31.8731,
   10.6237,
   31.8360,
    4.9594,
    4.4516,
   22.2763,
   -0.0000,
   20.5038,
    3.8583,
   19.3651,
    4.8838,
   11.0972,
    7.4617,
    1.4769,
    2.7192,
   10.9269,
    8.3487,
   52.7819,
   13.3573])

from sklearn.linear_model import LinearRegression as LR

model1 = LR().fit(X,y)

import matplotlib.pyplot as plt

plt.plot(X[:,0],model1.predict(X))
plt.scatter(X[:,0],y,color = 'red')
plt.show()

Answer 1

plt.plot() function draws lines in the order you give in. In order to draw regression line you need to input your X values and predictions in the order of min to max of X. Simplest way to do that would be:

predictions = model1.predict(X)
order = X[:,0].argsort()
predictions = predictions[order]
x = X[:,0][order]


plt.plot(x,predictions)
plt.scatter(X[:,0],y,color = 'red')
plt.show()

Answer 2

Is this what you are going for?

import numpy as np
from sklearn.linear_model import LinearRegression as LR
import matplotlib.pyplot as plt


model1 = LR().fit(X,y)

preds = model1.predict(X)


plt.scatter(preds, y)

xpoints = ypoints = plt.xlim()
plt.plot(xpoints, ypoints, linestyle='--', color='k')
plt.show()