Variance, standard deviation, covariance, correlation coefficient of variance, standard deviation, covariance, correlation coefficient

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Variance, standard deviation, covariance, correlation coefficient

 

【variance】

　　(Variance) is a measure of the probability theory and statistical variance of the random variable measure of the degree of dispersion of time or a set of data. Probability theory is used to measure the variance of random variables and its mathematical expectation (ie mean ) between the degree of deviation. Statistics of variance (sample variance) is the square of the difference between the value of the average value of each sample and all the sample values average . In many practical problems, the study is significant variance that is, the degree of deviation. Variance is a measure of the source data and measure the difference between the expected value. (Baidu Encyclopedia)

　　

　　Statistical description, the variance used to calculate the difference between each variable (observed value) and the overall mean. To avoid deviation from the mean zero sum, sum of squares of deviations from the mean affected sample size, using the average statistical degree of variation from the mean square difference and the variables described. The overall variance calculation formula:

　　             

　　In practice, when the overall mean is difficult to obtain, instead of the overall sample statistics applied parameters, corrected by the sample variance of the formula:

　　^ 2 = [Sigma S (X-   ) ^ 2 / (n--. 1) S ^ 2 is the sample variance, X is a variable,   to the sample mean, sample n-number of cases. (Unbiased estimate)

[Standard deviation]

　　Standard deviation (Standard Deviation), Chinese environment has often called mean square deviation is the square of the deviation from the mean square root of the arithmetic mean, expressed as σ. The standard deviation is the square root of the variance of the arithmetic. Standard deviation reflects the degree of dispersion of a data set. Mean same two sets of data, not necessarily the same standard deviation. Standard deviation also referred to as a standard deviation , or standard deviation experiment, formula

　　   

【Covariance】

　　It can be understood as popular: two variables change in the same direction in the process of change, or changes in the opposite direction, the same direction or reverse what extent?

　　You become big, I also increases, indicating that the two variables change in the same direction, then the covariance is positive.

　　You become larger, and I become smaller, indicating that the two variables is the reverse change, then the covariance is negative.

　　From the numerical perspective, the greater the value covariance, two variables larger extent also in the same direction. vice versa.

　　

　　Translate simple formula is: If you have X, Y two variables, "the difference between the mean of X-value" Every time multiplied by the "Y value of its mean, (in fact, is seeking" expects, "but not too much new extended concept, and is averaging a simple thought).

[Correlation]

　　Correlation is a non-deterministic correlation coefficients between the study variables are linearly related to the amount of degree. Since the object of different studies, there are several correlation coefficients defined manner. Simple correlation coefficient: also known as linear correlation coefficient, or correlation coefficient, r is generally expressed by letters, used to measure the linear relationship between two variables.

　　 　　Is to use X, Y covariance divided by the standard deviation of X and Y standard deviation. Therefore, the correlation coefficient covariance can also be seen as: a knockout of two dimensionless variables influence, special covariance normalized.

　　Since it is a special kind of covariance, that it:

　　1, can also reflect upon two variables change in the same direction or reverse, if it is a positive change in the same direction, the reverse change will be negative.

　　2, because it is the covariance normalized, so the more important characteristics: it eliminates the effect of changes in the amplitude of the two variables, but simply a reaction similar to the extent of changes in two variables per unit.

 

 【references】

https://www.zhihu.com/question/20852004

https://baike.baidu.com/item/%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0/3109424?fr=aladdin

https://blog.csdn.net/u010182633/article/details/45921929

https://www.zhihu.com/question/20099757

【variance】

　　(Variance) is a measure of the probability theory and statistical variance of the random variable measure of the degree of dispersion of time or a set of data. Probability theory is used to measure the variance of random variables and its mathematical expectation (ie mean ) between the degree of deviation. Statistics of variance (sample variance) is the square of the difference between the value of the average value of each sample and all the sample values average . In many practical problems, the study is significant variance that is, the degree of deviation. Variance is a measure of the source data and measure the difference between the expected value. (Baidu Encyclopedia)

　　

　　Statistical description, the variance used to calculate the difference between each variable (observed value) and the overall mean. To avoid deviation from the mean zero sum, sum of squares of deviations from the mean affected sample size, using the average statistical degree of variation from the mean square difference and the variables described. The overall variance calculation formula:

　　             

　　In practice, when the overall mean is difficult to obtain, instead of the overall sample statistics applied parameters, corrected by the sample variance of the formula:

　　^ 2 = [Sigma S (X-   ) ^ 2 / (n--. 1) S ^ 2 is the sample variance, X is a variable,   to the sample mean, sample n-number of cases. (Unbiased estimate)

[Standard deviation]

　　Standard deviation (Standard Deviation), Chinese environment has often called mean square deviation is the square of the deviation from the mean square root of the arithmetic mean, expressed as σ. The standard deviation is the square root of the variance of the arithmetic. Standard deviation reflects the degree of dispersion of a data set. Mean same two sets of data, not necessarily the same standard deviation. Standard deviation also referred to as a standard deviation , or standard deviation experiment, formula

　　   

【Covariance】

　　It can be understood as popular: two variables change in the same direction in the process of change, or changes in the opposite direction, the same direction or reverse what extent?

　　You become big, I also increases, indicating that the two variables change in the same direction, then the covariance is positive.

　　You become larger, and I become smaller, indicating that the two variables is the reverse change, then the covariance is negative.

　　From the numerical perspective, the greater the value covariance, two variables larger extent also in the same direction. vice versa.

　　

　　Translate simple formula is: If you have X, Y two variables, "the difference between the mean of X-value" Every time multiplied by the "Y value of its mean, (in fact, is seeking" expects, "but not too much new extended concept, and is averaging a simple thought).

[Correlation]

　　Correlation is a non-deterministic correlation coefficients between the study variables are linearly related to the amount of degree. Since the object of different studies, there are several correlation coefficients defined manner. Simple correlation coefficient: also known as linear correlation coefficient, or correlation coefficient, r is generally expressed by letters, used to measure the linear relationship between two variables.

　　 　　Is to use X, Y covariance divided by the standard deviation of X and Y standard deviation. Therefore, the correlation coefficient covariance can also be seen as: a knockout of two dimensionless variables influence, special covariance normalized.

　　Since it is a special kind of covariance, that it:

　　1, can also reflect upon two variables change in the same direction or reverse, if it is a positive change in the same direction, the reverse change will be negative.

　　2, because it is the covariance normalized, so the more important characteristics: it eliminates the effect of changes in the amplitude of the two variables, but simply a reaction similar to the extent of changes in two variables per unit.

 

 【references】

https://www.zhihu.com/question/20852004

https://baike.baidu.com/item/%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0/3109424?fr=aladdin

https://blog.csdn.net/u010182633/article/details/45921929

https://www.zhihu.com/question/20099757