pandas相关系数和协方差Titanic

pandas相关系数和协方差.

import pandas as pd
import numpy as np

df=pd.read_csv("/content/train.csv")

df

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891 rows × 12 columns

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const buttonEl =
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buttonEl.style.display =
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async function convertToInteractive(key) {
const element = document.querySelector(‘#df-aa2392b6-ff11-4264-84ef-734f69abd0b0’);
const dataTable =
await google.colab.kernel.invokeFunction(‘convertToInteractive’,
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if (!dataTable) return;

const docLinkHtml = ‘Like what you see? Visit the ‘ +
‘<a target=”_blank” href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook’
+ ‘ to learn more about interactive tables.’;
element.innerHTML = ‘’;
dataTable[‘output_type’] = ‘display_data’;
await google.colab.output.renderOutput(dataTable, element);
const docLink = document.createElement(‘div’);
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}

一.协方差
只表示线性相关的方向，取值正无穷到负无穷。
也就是说，协方差为正值，说明一个变量变大另一个变量也随之变大（正相关）；取负值说明一个变量变大另一个变量变小（负相关），取0说明两个变量没有相关关系。

注意：协方差的绝对值不反映线性相关的程度（其绝对值与变量的取值范围有关系）。

二.相关系数
不仅表示线性相关的方向，还表示线性相关的程度，取值[-1,1]。

也就是说，相关系数为正值，说明一个变量变大另一个变量也变大；取负值说明一个变量变大另一个变量变小，取0说明两个变量没有相关关系。
同时，相关系数的绝对值越接近1，线性关系越显著。
通常情况下，当相关系数的绝对值大于2/sqrt(N)，N为样本点的数量时，我们认为线性关系是存在的。

协方差确定两个变量的关系，即正相关，负相关/无关
相关系数确定两个变量的关系&相关程度

协方差计算

dataframe.cov(): 计算所有变量之间的协方差

df.cov()

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}

.colab-df-container {
display:flex;
flex-wrap:wrap;
gap: 12px;
}

.colab-df-convert {
background-color: #E8F0FE;
border: none;
border-radius: 50%;
cursor: pointer;
display: none;
fill: #1967D2;
height: 32px;
padding: 0 0 0 0;
width: 32px;
}

.colab-df-convert:hover {
background-color: #E2EBFA;
box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);
fill: #174EA6;
}

[theme=dark] .colab-df-convert {
background-color: #3B4455;
fill: #D2E3FC;
}

[theme=dark] .colab-df-convert:hover {
background-color: #434B5C;
box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);
filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));
fill: #FFFFFF;
}

const buttonEl =
document.querySelector(‘#df-a2f5a22f-3aaf-4025-b37d-2598d4b131f6 button.colab-df-convert’);
buttonEl.style.display =
google.colab.kernel.accessAllowed ? ‘block’ : ‘none’;

async function convertToInteractive(key) {
const element = document.querySelector(‘#df-a2f5a22f-3aaf-4025-b37d-2598d4b131f6’);
const dataTable =
await google.colab.kernel.invokeFunction(‘convertToInteractive’,
[key], {});
if (!dataTable) return;

const docLinkHtml = ‘Like what you see? Visit the ‘ +
‘<a target=”_blank” href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook’
+ ‘ to learn more about interactive tables.’;
element.innerHTML = ‘’;
dataTable[‘output_type’] = ‘display_data’;
await google.colab.output.renderOutput(dataTable, element);
const docLink = document.createElement(‘div’);
docLink.innerHTML = docLinkHtml;
element.appendChild(docLink);
}

相关系数计算

dataframe.corr():计算所有变量之间的相关系数

df.corr()

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vertical-align: middle;
}

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vertical-align: top;
}

.dataframe thead th {
text-align: right;
}

.colab-df-container {
display:flex;
flex-wrap:wrap;
gap: 12px;
}

.colab-df-convert {
background-color: #E8F0FE;
border: none;
border-radius: 50%;
cursor: pointer;
display: none;
fill: #1967D2;
height: 32px;
padding: 0 0 0 0;
width: 32px;
}

.colab-df-convert:hover {
background-color: #E2EBFA;
box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);
fill: #174EA6;
}

[theme=dark] .colab-df-convert {
background-color: #3B4455;
fill: #D2E3FC;
}

[theme=dark] .colab-df-convert:hover {
background-color: #434B5C;
box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);
filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));
fill: #FFFFFF;
}

const buttonEl =
document.querySelector(‘#df-637b0494-27fe-47a3-ad8d-06e1656c073d button.colab-df-convert’);
buttonEl.style.display =
google.colab.kernel.accessAllowed ? ‘block’ : ‘none’;

async function convertToInteractive(key) {
const element = document.querySelector(‘#df-637b0494-27fe-47a3-ad8d-06e1656c073d’);
const dataTable =
await google.colab.kernel.invokeFunction(‘convertToInteractive’,
[key], {});
if (!dataTable) return;

const docLinkHtml = ‘Like what you see? Visit the ‘ +
‘<a target=”_blank” href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook’
+ ‘ to learn more about interactive tables.’;
element.innerHTML = ‘’;
dataTable[‘output_type’] = ‘display_data’;
await google.colab.output.renderOutput(dataTable, element);
const docLink = document.createElement(‘div’);
docLink.innerHTML = docLinkHtml;
element.appendChild(docLink);
}

series.corr(series): 计算指定变量之间的协方差

df['Age'].corr(df['Pclass'])

-0.36922601531551724

https://colab.research.google.com/drive/1fEha3cjo3noLYCnLO8-RCIEGMjW6nxnq#scrollTo=6O1CulKF16lL