9.1.1 Correlation analysis: exploring the connection of things 相关分析：初探事物联系在线视频

怎么了 这么不高兴
You look upset What's up

新鞋被人踩了呀
The new shoes were stamped by someone

昨天作业做到十一点半
I did homework until half-past eleven yesterday

今天六点半老妈就把我叫起来
Mom woke me up at half-past six today

一天都没精神
I lack energy all day long

下午还考了个试
and took a test in the afternoon

人生一点都不幸福
Life is not happy at all

是吗 不过确实 睡的少了
Really? But you sleep less indeed

人生是不幸福
Life is unhappy

姐 你说新闻里不天天说
Sister, haven't you said the news promises every day

要给我们一个幸福的童年吗
we shall be given a happy childhood

作业那么多
With so much homework

睡觉都睡不够
and so little sleep

哪里会幸福啊
how can we feel happy

我就想天天睡觉 睡的饱饱的
I just feel like sleeping to the full every day

恩 其实睡的多了也不幸福
Hum, actually neither sleeping much

睡的少了也不幸福
nor sleeping little promises happiness

不多不少最幸福
but just the modest amount will do

你等等 给你看个图
Wait, Let me show you a graph

傻二妞 你来看
Silly girl, come and see

这个图上 横轴代表睡眠时间的长短
In this graph, the horizontal axis represents the duration of sleep

纵轴代表幸福感
whereas the vertical axis represents a sense of happiness

这个位置幸福感最强
Happiness is most strongly felt in this position

大概是睡十个小时吧
Roughly ten hours of sleep

所以睡的太多或睡的太少
So sleeping too much or too little

都没有那么幸福
is not that happy

我要把这个图给老师看看
I will show this graph to my teacher

姐 这些点是不是隐隐约约的
Sister, are these points indistinct

可以连成一条线 你看
Look, They can be connected to a line

行啊 这都看出来了
Great, You can see that

这个在统计学上
This is called the regression line

叫回归线
in statistics

我现在做的就是一个
What I am working on now is a

非线性回归方程
nonlinear regression equation

姐 说人话行吗
Sister, can you talk like a human being

你听不懂的
You don’t understand

这是统计学回归分析的内容
This is something about statistical regression analysis

姐刚学过
I have just learned

我也要学
I also want to learn

大家学的时候
When everyone was learning

这个相关分析和回归分析
the correlation analysis and regression analysis

是连在一起的
are connected together

相关分析是研究现象
The correlation analysis is an analytic method

与现象之间的
to explore the relation

一种关系的分析方法
between phenomena

后面回归分析就是
whereas the regression analysis later

来反映变量
reflects

一个变量的变化
to what extent

会导致另外一个变量
the variation of a variable

多大幅度的变化
could cause the variation of another

这是回归分析的内容
This is the content of regression analysis

我们知道社会 经济 自然等等现象
We know social, economic, natural and other phenomena

它们现象与现象之间
Between one phenomenon and another

有许多种的关系
there are a lot of relations

比如说在我们社会学研究中
For instance, in the sociological research

我们研究人与人之间的关系的时候
while studying the interpersonal relations

我们可以采用
we can adopt the following method

比如说我们在火车上
Say we are on the train

随机选一百个人
where one hundred people are selected at random

选一百个人
Among the one hundred people

每个人写出自己十个熟悉人的名字
everyone writes ten names familiar to him/her

我们凑在一起
We put them together

这里至少有一个人
There is at least one individual

大家都认识
everyone recognizes

这就能反映我们人与人之间的关系
This can reflect the interpersonal relation

社会学还有一种调查方法
Another investigation method in sociology

也是研究人与人之间的关系的
is also employed to study interpersonal relations

比如说我寄一份材料或者是物品
For example, I have material or goods to send

给我一个熟人 他在新疆
to an acquaintance in Sinkiang

而我不直接寄给他
Instead of sending to him directly

只是告诉这些人
I inform someone

我这个收件人的姓名是什么
what is the name of this recipient

我就先寄给湖南一个朋友
So I send first to a friend in Hunan

他不认识这个人
who does not know the recipient

但是他也可以寄给他的认识的人
but who can send it to someone he knows

就这样一直往下寄下去
The article is sent down like this

好像一般研究的情况是这样
It looks like the situation of general research

就寄到第六个人的时候
Until the sixth person

他可以把这个物件
he can send the article

要寄到我想寄的那个人
to the person I am intended to

这就是说明了人与人之间的关系
This explains the relationship between people

比较密切
is rather close

以社会学研究人与人之间的关系
The relation between people is studied from a sociological perspective

我们现在相关分析里面
In our correlation analysis now

大多数研究的是我们经济关系
most studies focus on our economic relations

社会关系 自然关系等等
social relations, natural relations, etc.

在研究这些关系的时候
While studying these relations

我们一般大多数情况下
we typically and mostly

是用我们的理论分析
resort to the theoretical analysis

而在我们统计里面
In statistics

研究现象与现象之间关系的时候
while studying the relation between phenomena

我们用的是数量分析
we resort to quantitative analysis

就研究现象与现象之间的数量关系
namely studying the qualitative relation between phenomena

而现象与现象之间的数量关系
While the qualitative relation between phenomena

或者我们就讲
or simply deemed

变量与变量之间的数量关系
the qualitative relation between variables

一般来讲
generally

是体现为两种关系
manifests in two kinds of relations

一种是函数关系
The first is functional relations[M1]

函数关系大家在数学里面看到的
as observed in mathematics

比如说圆的面积
such as the relation between the area of a circle

与圆的半径之间的关系
and the radium of the circle

它有一个公式
for which there is a formula

它这里的特点就是
Its characteristic is

一个就是自变量变动一个单位
as the independent variable varies by a unit

应变量是唯一的一个数值
the dependent variable varies in correspondence

与它对应进行变动
to it at a single value

而除掉函数关系以外
Aside from functional relations[M2]

社会 经济 自然现象里面
in social, economic, and natural phenomena

还存在另外一种数量关系
there exists another kind of qualitative relations

而那种数量关系
which is

就是我们讲的统计关系
the statistical relations we have related

也就是我们这节课要讲的相关关系
also referred to as the correlation we will be discussing in this lecture

相关分析就是分析这种关系
Correlation analysis deals with this kind of relations

那变量与变量之间的关系有哪些呢
So what are the relations between variables

我们大家了解比较多的
What is familiar to us

那就是因果关系
is the causal relation[M3]

因果关系指的就是说
The causal relation[M4] involves

有原因变量 有结果变量
the causal variable and the outcome variable

研究这两个变量的关系
The relation between the two variables is studied

因果关系分两类
The causal relation is classified into two types:

一类是单向因果
One is one-way causation

一类是双向因果
the other being two-way causation

单向因果就是说
The one-way causation suggests

原因的产生 原因的出现
the generation and emergence of a cause

必然导致结果的产生 结果的出现
leads inevitably to the generation and emergence of an outcome

比如说我们讲
For instance, if we

父母的身高是原因的话
attribute parents’stature to be a cause

小孩的身高 高 这就是结果
then the child’s stature is the outcome

这个关系就属于单向因果
This relation belongs to the one-way causation

双向因果是说出发点
The two-way causation

是X变量的基础上
on the base that the starting point is variable X

来研究X变化对Y产生的影响
studies the effect of the variation in X on Y

那么X是原因 Y是结果
Then X is the cause whereas Y is the outcome

反过来我站在Y的角度
Conversely, from the angle of Y

来研究Y的变化对X产生的影响
when the focus is shifted on the effect of the variation in Y on X

那么Y就是原因 X就是结果变量
Y is the cause whereas X is the outcome variable

那这种双向因果
Such a two-way causation

在我们经济学里面是有的
is covered in economics

比如说我们经济学
A case-in-point in economics

研究销售量与销售价格之间的关系
is the study on the relationship between sales volume and sales price

你如果说我们把价格看成是原因
Deeming price as the cause

把销售量看成是结果
and sales volume as the outcome

我们可以构造一个模型
we can build a model

就是销售量它的变化
in which the variation in sales volume

是由价格来进行变化解释的
is explained by the variation in price

这种相关回归分析模型
Such a model of correlation regression analysis

当然我们在经济学里面知道
is known to us in economics

价格的变化会受销售量的影响
The variation in price would be affected by sales volume

销售量越高 价格越低
The higher the sales volume the lower the price

那时候如果你反过来
In the opposite way

我也研究销售量的多少
I also study the effect of sales volume

对价格产生的影响
on price

那销售量那就是原因
Then sales volume is the cause

价格变化就属于结果
whereas price variation is the outcome

这是我们讲的因果关系
This is the so-called causal relation

但是我们的相关分析跟因果分析
However, there is a substantial distinction

还是有本质的区别
between correlation analysis and causal analysis

相关分析讲的是相关关系的
Correlation analysis deals with an analytic method

一种分析方法
for correlation

相关关系指的是什么
What does correlation refer to

指的是变量与变量之间
It refers to, in the first place

它存在一种数量关系 这是其一
a qualitative relation between variables;

其二
in the second place

这种数量关系跟函数关系里面
such a qualitative relation is different from

它有不同
the functional relation

X变动的时候
As X varies

它每变动一个单位
by one unit

Y是不是按照唯一的数值出现呢
does Y correspond

来进行对应呢 不是
at a single value No

我们比如说身高与体重之间的关系
For example, the relation between body height and weight

我们大家知道一般来讲
Generally, as we know

身高越高的人体重越重
the greater one’s height the greater one’s weight

但是并不是说
But it does not mean

我身高增加一厘米
as my height increases by 1 cm

体重就增加05公斤吗 不一定
my weight increases by 05 kg Not always

因为身高跟体重之间的关系
Because the relation between body height and weight

里面还有其他因素的影响
is also subject to other factors

比如说我们的遗传
such as genetic

饮食 睡眠等等等等
dietary, sleep, and other factors

都会影响他们之间的一些
all of which can make a difference to

严格的或者精确的对应关系
the rigorous or precise correspondence between them

那我们要研究
So while studying

身高与体重之间的关系的时候
the relation between body height and weight

我们在相关分析的时候
and performing correlation analysis

就要找出一组数据
we shall find a set of data

比如一组数据的体重
say a set of data of weights

对应一组数据的身高
corresponding to a set of data of heights

或者是比如说身高一米七的人
or say someone’s height of 170 cm

对应的体重有65公斤的
may correspond to a weight of 65 kg

有60公斤的
60 kg

有67公斤的 有63公斤的
67 kg, or 63 kg

那么一米七的身高对应的体重
So the weight to which the 170 cm height corresponds

它是一个平均的体重
is an average weight

我们再按照这个思路去研究的话
Going deep along this train of thought

我们就能发现身高越高
we will find the greater the height

体重就越重
the greater the weight

这种关系就叫做相关关系
Such a relation is called the correlation

也叫做统计关系
or statistical relation

所以我们可以总结一下
So we can make a summary

相关关系或者叫统计关系
Correlation or statistical relation

指的是变量与变量之间的
refers to a qualitative relation of average significance

一种平均的数量关系
between variables

下面我们来看一下
Below let’s take a look at

相关关系的种类
the kinds of correlation

相关关系有哪几种呢
What are the kinds of correlation

我们先从变量的个数来分析
Let’s begin with the number of variables

如果说只研究两个变量之间的关系
If the relation between only two variables is studied

那就是单相关
then it is single correlation

两个叫X与Y之间的变量关系
The relation between two variables, X and Y

那就属于单相关
is a single correlation

比如说我们研究父母的身高X
For example, the relation between parents’ stature X

与子女的身高Y之间的关系
and offspring’s stature Y

这属于单相关关系
is a single correlation

还有一种是变量比较多
Still another kind of correlation involves relatively many variables

比如我们研究一个变量
For example, the relation between one variable

与有N个变量之间的关系
and N variables

那这种关系就属于复相关
is a multiple correlation

比如说婴儿的智力
For example, what factors

与哪些因素有关
is an infant’s intellect corelated to

我们知道与父亲 母亲的智商有关
As we know, it is correlated to the intellects of its biological father and mother

与他出生的年月有关
to its month and year of birth

与父母的年龄差别有关
to the age gap between parents

与小孩的带他第一个保姆的水平
to the level of the first babysitter with the kid

等等等等这些都有关系
and so on so forth

我们发现婴儿智商与下面
We find an infant’s IQ is correlated to the following

就是X{\fs12}i{\r}里面的X{\fs12}i{\r}
namely X{\fs12}i{\r} in X{\fs12}i{\r}

研究到目前为止
Up till now

研究到了五十多个因素有关
research has identified more than fifty correlative factors

那我们比如说Y与X{\fs12}i{\r}之间的关系
The relation between Y and X{\fs12}i{\r}, for example

就属于复相关
is a multiple correlation

那有了复相关
There being multiple correlation

我们大家自然而然就会想到
everyone would naturally come up with

另外还有一种相关
another kind of correlation

跟变量的多少

那就是一个偏相关
namely partial correlation

偏相关 偏就是部分的意思
Where ‘partial’ means part

就是我们成语来讲
We have a Chinese idiom

以偏概全的偏 它是部分
take a part for the whole

就是说比如说我只研究
For example, the relation

母亲的智商与小孩的智商的关系
between the mother’s IQ and child’s IQ

那就是X{\fs12}1{\r}与Y之间的关系
is actually the relation between X{\fs12}1{\r} and Y

那这种关系就叫做偏相关分析
Such a relation is called partial correlation analysis

这是相关分析的第一种分类
Above is the first classification of correlation analysis

用变量的个数来进行分
It is classified in terms of the number of variables

有单相关 复相关 偏相关
and into single correlation, multiple correlation, and partial correlation

第二 看变量与变量之间的
Second, depending on the ______ between variables

也就是它们的方向来看
namely their direction

有正相关
there is the positive correlation

就是X与Y之间的关系
where X and Y

它们是同方向发生变化
vary in the same direction

就X增加 Y也增加
namely as X increases Y increases

X减少 Y也减少
as X decreases Y decreases

那这个关系就属于正相关
This relation is a positive correlation

比如我身高与体重之间的关系
For example, the relation between my body height and weight

它就属于正相关
is a positive correlation

还有一种是反的
Another is the opposite

就是X的变化与Y的变化
specifically, Y varies in the opposite direction

是相互反的
as X does

X增加 Y减少
As X increases Y decreases;

Y增加 X减少
as Y increases X decreases

那这个属于负相关
This is a negative correlation

在我们社会经济现象中
In socioeconomic phenomena

这种例子也比较多
such cases are ample

这是按方向分
This is a classification by direction

再按它的线性关系分
Classified by linear relation

我们有线性相关
there are linear correlation

和非线性相关
and nonlinear correlation

线性相关和非线性相关就是说
Linear correlation and nonlinear correlation mean

它X与Y的变化
as X and Y vary

它们的关系是线性关系
the relation between them is linear

还是非线性关系
or nonlinear relation

在社会经济现象里面
In socioeconomic phenomena

X与Y的关系
The relation between X and Y

我们大多数表现为
is mostly manifested as

经济的里面表现为非线性关系
nonlinear relation in economics

所以我们在经济研究中
So in economic research

我们的相关分析里面
in correlation analysis

大部分表现为线性 非线性的
most are manifested as linear or nonlinear

当然非线性的处理的时候
Of course, there is a methodology

处理为线性的时候
to treat the nonlinear cases

它有一套办法
as if they were the linear cases

非线性的里面
In nonlinear correlation

一般我们可以证明
generally we can prove

它属于非齐次的二次
it fits the nonhomogeneous quadratic form

而且只是二次的非齐次
and just the quadratic nonhomogeneous form

相关分析里面的第四个分类
The fourth classification in the correlation analysis

它就是按它相关程度分
is performed by degree of correlation

第一 有完全相关
First, the complete correlation

完全相关就是我们讲的函数关系
is what we refer to as the functional relation

X与Y的关系
The relation between X and Y

是一一对应的关系
is one-to-one correspondence

等一下我们讲到相关系数的时候
When talking of correlation coefficient later

就发现它的相关系数可能是正负一
we will find its correlation coefficient may be ±1

这是完全关系
This is about the complete correlation

那就是我们的函数关系
the so-called functional relation

还有一种就是不相关
Another kind is noncorrelation

就是X与Y之间没有任何关系
meaning there is not any relation between X and Y

就是X变化 Y不变
As X varies Y remains unchanged

或者Y变动 X不变
or as Y varies X remains unchanged

那么这个时候它们两个就不相关
At the moment both are uncorrelated

我们叫不相关的
We say the correlation coefficient

完全不相关的
in the noncorrelation or complete noncorrelation

它的相关系数是等于零
equals zero

那大部分情况我们讲的
In most cases

就是我们讲的那种相关
of correlation

它的计算以后
the correlation coefficient

我们看了相关系数的公式
calculated by formula

我们计算出来的结果
may range

它可能是在正负一之间
between -1 and 1

那就是我们讲的相关程度分的
That is about the analysis we discuss on the degree of correlation
[M1]functional relationship
[M2]functional relationship
[M3]causality
[M4]causality