"如何添加一條最適合散點圖的線"

Question

我目前正在使用 Pandas 和 matplotlib 來執行一些數據可視化，我想在我的散點圖中添加一條最適合的線。

這是我的代碼：

import matplotlib
import matplotlib.pyplot as plt
import pandas as panda
import numpy as np

def PCA_scatter(filename):

   matplotlib.style.use('ggplot')

   data = panda.read_csv(filename)
   data_reduced = data[['2005', '2015']]

   data_reduced.plot(kind='scatter', x='2005', y='2015')
   plt.show()

PCA_scatter('file.csv')

Answer 1

您可以使用Seaborn一舉完成整個擬合和情節。

import pandas as pd
import seaborn as sns
data_reduced= pd.read_csv('fake.txt',sep='\s+')
sns.regplot(data_reduced['2005'],data_reduced['2015'])

Answer 2

您可以使用np.polyfit()和np.poly1d() 。 使用相同的x值估計一階多項式，並添加到由.scatter()圖創建的ax對象。 使用示例：

import numpy as np

     2005   2015
0   18882  21979
1    1161   1044
2     482    558
3    2105   2471
4     427   1467
5    2688   2964
6    1806   1865
7     711    738
8     928   1096
9    1084   1309
10    854    901
11    827   1210
12   5034   6253

估計一次多項式：

z = np.polyfit(x=df.loc[:, 2005], y=df.loc[:, 2015], deg=1)
p = np.poly1d(z)
df['trendline'] = p(df.loc[:, 2005])

     2005   2015     trendline
0   18882  21979  21989.829486
1    1161   1044   1418.214712
2     482    558    629.990208
3    2105   2471   2514.067336
4     427   1467    566.142863
5    2688   2964   3190.849200
6    1806   1865   2166.969948
7     711    738    895.827339
8     928   1096   1147.734139
9    1084   1309   1328.828428
10    854    901   1061.830437
11    827   1210   1030.487195
12   5034   6253   5914.228708

和情節：

ax = df.plot.scatter(x=2005, y=2015)
df.set_index(2005, inplace=True)
df.trendline.sort_index(ascending=False).plot(ax=ax)
plt.gca().invert_xaxis()

要得到：

還提供了線方程：

'y={0:.2f} x + {1:.2f}'.format(z[0],z[1])

y=1.16 x + 70.46

Answer 3

另一種選擇（使用np.linalg.lstsq ）：

# generate some fake data
N = 50
x = np.random.randn(N, 1)
y = x*2.2 + np.random.randn(N, 1)*0.4 - 1.8
plt.axhline(0, color='r', zorder=-1)
plt.axvline(0, color='r', zorder=-1)
plt.scatter(x, y)

# fit least-squares with an intercept
w = np.linalg.lstsq(np.hstack((x, np.ones((N,1)))), y)[0]
xx = np.linspace(*plt.gca().get_xlim()).T

# plot best-fit line
plt.plot(xx, w[0]*xx + w[1], '-k')

Answer 4

這涵蓋了plotly方法

#load the libraries

import pandas as pd
import numpy as np
import plotly.express as px
import plotly.graph_objects as go

# create the data
N = 50
x = pd.Series(np.random.randn(N))
y = x*2.2 - 1.8

# plot the data as a scatter plot
fig = px.scatter(x=x, y=y) 

# fit a linear model 
m, c = fit_line(x = x, 
                y = y)

# add the linear fit on top
fig.add_trace(
    go.Scatter(
        x=x,
        y=m*x + c,
        mode="lines",
        line=go.scatter.Line(color="red"),
        showlegend=False)
)
# optionally you can show the slop and the intercept 
mid_point = x.mean()

fig.update_layout(
    showlegend=False,
    annotations=[
        go.layout.Annotation(
            x=mid_point,
            y=m*mid_point + c,
            xref="x",
            yref="y",
            text=str(round(m, 2))+'x+'+str(round(c, 2)) ,
        )
    ]
)
fig.show()

fit_line在哪里

def fit_line(x, y):
    # given one dimensional x and y vectors - return x and y for fitting a line on top of the regression
    # inspired by the numpy manual - https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html 
    x = x.to_numpy() # convert into numpy arrays
    y = y.to_numpy() # convert into numpy arrays

    A = np.vstack([x, np.ones(len(x))]).T # sent the design matrix using the intercepts
    m, c = np.linalg.lstsq(A, y, rcond=None)[0]

    return m, c

Answer 5

上面的最佳答案是使用seaborn。 要添加到上面，如果您使用循環創建許多圖，您仍然可以使用 matplotlib

    import pandas as pd
    import seaborn as sns
    import matplotlib.pyplot as plt

    data_reduced= pd.read_csv('fake.txt',sep='\s+')
    for x in data_reduced.columns:
        sns.regplot(data_reduced[x],data_reduced['2015'])
        plt.show()

plt.show() 將暫停執行，以便您可以一次查看一個圖

Answer 6

只是為了補充（更新羅伯特卡爾霍恩的答案）。 如果您不指定 x,y，您現在將在新版本的 pandas 上收到未來警告。

FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.