Covariance and correlation

Covariance and correlation

In probability theory and statistics, the mathematical concepts of covariance and correlation are very similar. Both describe the degree to which two random variables or sets of random variables tend to deviate from their expected values in similar ways. If X and Y are two random variables, with means (expected values) μX and μY and standard deviations σX and σY, respectively, then their covariance and correlation are as follows: so that where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as the square of the standard deviation. The correlation of a variable with itself is always 1 (except in the degenerate case where the two variances are zero because X always takes on the same single value, in which case the correlation does not exist since its computation would involve division by 0). More generally, the correlation between two variables is 1 (or –1) if one of them always takes on a value that is given exactly by a linear function of the other with respectively a positive (or negative) slope. Although the values of the theoretical covariances and correlations are linked in the above way, the probability distributions of sample estimates of these quantities are not linked in any simple way and they generally need to be treated separately. (Wikipedia).

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Covariance Definition and Example

What is covariance? How do I find it? Step by step example of a solved covariance problem for a sample, along with an explanation of what the results mean and how it compares to correlation. 00:00 Overview 03:01 Positive, Negative, Zero Correlation 03:19 Covariance for a Sample Example

From playlist Correlation

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From playlist COVARIANCE AND VARIANCE

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Covariance (8 of 17) What is the Correlation Coefficient?

Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn what is and how to find the correlation coefficient of 2 data sets and see how it corresponds to the graph of the data

From playlist COVARIANCE AND VARIANCE

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From playlist Statistics: Introduction

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Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will find the correlation coefficients of the 3 data sets form the previous 2 videos. Next video in this series can be seen at:

From playlist COVARIANCE AND VARIANCE

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Covariance (14 of 17) Covariance Matrix "Normalized" - Correlation Coefficient

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From playlist COVARIANCE AND VARIANCE

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From playlist Level 1 Chartered Financial Analyst (CFA ®) Volume 1

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From playlist Quantitative Analysis (FRM Topic 2)

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Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will calculate the correlation coefficients of 2 separate 2 data sets and graph the 2 graphs and see how the graphs corresponds t

From playlist COVARIANCE AND VARIANCE

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Related pages

Variance | Covariance matrix | Random variable | Stationary process | Expected value | Correlation | Probability theory | Time series | Linear function | Autocorrelation | Standard deviation | Mean | Statistics | Cross-correlation | Autocovariance | Covariance | Cross-covariance