请教,皮尔逊相关系数,数学原理

LeonTown 2009-06-02 10:24:50
如题,
请教,皮尔逊相关系数公式的数学原理。

谢谢!
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无敌小猫猫 2012-08-09
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找到别人的一篇博客,推荐一下。http://blog.csdn.net/wsywl/article/details/5727327
mengliangabc 2010-03-21
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请问什么叫自相关系数呢?
lantianbaiyun1234 2009-07-09
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那我就不明白了,要是定序变量和定类变量怎么求相关,我说的是在EXCEL中
pstrunner 2009-06-02
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Pearson's Correlation Coefficient
This is one in a series of tutorials using examples from WINKS SDA.
Definition: Measures the strength of the linear relationship between two variables.

Assumptions: Both variables (often called X and Y) are interval/ratio and approximately normally distributed, and their joint distribution is bivariate normal.

Characteristics: Pearson's Correlation Coefficient is usually signified by r (rho), and can take on the values from -1.0 to 1.0. Where -1.0 is a perfect negative (inverse) correlation, 0.0 is no correlation, and 1.0 is a perfect positive correlation.

Related statistics: R2 (called the coefficient of determination or r squared) can be interpreted as the proportion of variance in Y that is contained in X.

Tests: The statistical significance of r is tested using a t-test. The hypotheses for this test are:

H0: rho = 0
Ha: rho <> 0

A low p-value for this test (less than 0.05 for example) means that there is evidence to reject the null hypothesis in favor of the alternative hypothesis, or that there is a statistically significant relationship between the two variables.

Note: This test is equivalent to the test of no slope in the simple linear regression procedure.

Location in WINKS: Pearson's correlation coefficient is found in the following locations:

1. Regression and Correlation - The Correlation procedure produces both Pearson and Spearman Correlation coefficients. The t-test for statistical significance of r is calculated. R2 is also reported.

2. Regression and Correlation - The Simple linear regression reports the Pearson correlation coefficient and the t-test. R2 is also reported.

3. Regression and Correlation - The Correlation Matrix procedure produces a matrix of correlations for a number of pairs of variables at a time, and includes the p-value for the test or significance of r.

Graphs: An important part of interpreting r is to observe a scatterplot of the data. Scatterplots are available from the Graphs option, as a part of Simple Linear Regression and in the Graphical Correlation Matrix option in Regression and Correlation.

url:
http://www.texasoft.com/winkpear.html
LeonTown 2009-06-02
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[Quote=引用 4 楼 gift_lbs 的回复:]
简单相关系数又称皮尔逊相关系数,它描述了两个定距变量间联系的紧密程度。样本的简单相关系数一般用r表示,计算公式为:
其中n 为样本量, 分别为两个变量的观测值和均值。r描述的是两个变量间线性相关强弱的程度。r的取值在-1与+1之间,若r>0,表明两个变量是正相关,即一个变量的值越大,另一个变量的值也会越大;若r<0,表明两个变量是负相关,即一个变量的值越大另一个变量的值反而会越小。r 的绝对值越大表明相关性越强…
[/Quote]

最终结果的使用,我知道~

但,我想知道的是,计算公式的数学意义!

谢谢!
gift_lbs 2009-06-02
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简单相关系数又称皮尔逊相关系数,它描述了两个定距变量间联系的紧密程度。样本的简单相关系数一般用r表示,计算公式为:
其中n 为样本量, 分别为两个变量的观测值和均值。r描述的是两个变量间线性相关强弱的程度。r的取值在-1与+1之间,若r>0,表明两个变量是正相关,即一个变量的值越大,另一个变量的值也会越大;若r<0,表明两个变量是负相关,即一个变量的值越大另一个变量的值反而会越小。r 的绝对值越大表明相关性越强,要注意的是这里并不存在因果关系。若r=0,表明两个变量间不是线性相关,但有可能是其他方式的相关(比如曲线方式)
利用样本相关系数推断总体中两个变量是否相关,可以用t 统计量对总体相关系数为0的原假设进行检验。若t 检验显著,则拒绝原假设,即两个变量是线性相关的;若t 检验不显著,则不能拒绝原假设,即两个变量不是线性相关的
LeonTown 2009-06-02
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[Quote=引用 2 楼 ibone 的回复:]
谢谢楼主
让我了解到一些概念
[/Quote]

你了解了吗?
给我讲讲。

知道多少,讲多少。
给你分!
ibone 2009-06-02
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谢谢楼主
让我了解到一些概念
LeonTown 2009-06-02
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顶一下

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