Covariance and Correlation

Thread starter asept
Start date May 3, 2009
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Correlation Covariance

In summary, covariance and correlation are both measures of the relationship between two variables, with covariance measuring the strength and direction and correlation measuring just the strength. They are calculated differently, with covariance being the average of the product of deviations and correlation being the covariance divided by the product of standard deviations. Positive values indicate a direct relationship while negative values indicate an inverse relationship. These measures can be useful in data analysis for understanding relationships and making predictions, but they have limitations such as only measuring linear relationships and not implying causation. Outliers can also heavily influence the results.

May 3, 2009

asept

I'm stuck on this problem:

Let X be uniform[0,1] and Y be uniform[0,X]. Calculate the covariance and correlation between X and Y.

thanks

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May 3, 2009

Defennder

Homework Helper

Just apply the definition of covariance and correlation. What are the formulae for both?

May 4, 2009

asept

Cov(X,Y) = E(XY) - E(X)E(Y)

May 5, 2009

Defennder

Homework Helper

Yes correct, and now just apply the formulae for E(X), E(Y) and E(XY). What formulae should you use to evaluate each?

1. What is the difference between covariance and correlation?

Covariance measures the relationship between two variables while correlation measures the strength and direction of that relationship. While covariance can range from negative infinity to positive infinity, correlation is always between -1 and 1.

2. How are covariance and correlation calculated?

Covariance is calculated by taking the average of the product of the deviations of two variables from their mean. Correlation is calculated by dividing the covariance by the product of the standard deviations of the two variables.

3. What do positive and negative covariance/correlation values indicate?

A positive covariance/correlation value indicates a direct relationship between the two variables, meaning that as one variable increases, the other variable also tends to increase. A negative covariance/correlation value indicates an inverse relationship, meaning that as one variable increases, the other variable tends to decrease.

4. How can covariance and correlation be used in data analysis?

Covariance and correlation can be used to understand the relationship between two variables and how they may affect each other. They can also be used to identify patterns and trends in data, as well as to make predictions and decisions based on the strength and direction of the relationship.

5. What are the limitations of using covariance and correlation?

Covariance and correlation can only measure linear relationships between variables. They also do not imply causation, meaning that a strong correlation does not necessarily mean that one variable causes the other. Additionally, outliers or extreme values can heavily influence the results of covariance and correlation calculations.