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The covariance between two variables is simply the average product of the values of two variables that have been expressed as deviations from their respective means. ------------------------------------------------------------------------------------------------- A worked example may be referenced at: http://math.info/Statistics/Covariance
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Why is covariance important?
Covariance is important because it measures the relationship between two variables. It indicates the direction and strength of the relationship between the variables. Covariance can help in understanding and predicting the behavior of variables and is widely used in statistics, finance, and economics.
Will the variance of the difference of two independent normally distributed random variables be equal to the SUM of the variances of the two distributions?
Yes it is. That is actually true for all random vars, assuming the covariance of the two random vars is zero (they are uncorrelated).
Where can one find information on the covariance matrix?
One can find information on the covariance matrix on the Wikipedia website where there is much information about the mathematics involved. One can also find information on Mathworks.
When do you use an F test?
When testing the sums of squares of variables which are independently identically distributed as normal variables. One of the main uses of the F-test is for testing for the significance of the Analysis of Variance (ANOVA) or of covariance.
Find the formula for percentage of covariance?
100 x (standard deviation/mean)
What do positive values of covariance indicate?
as the covariance of the two random variables (X and Y) is used for calculating the correlation coeffitient of those variables it indicates that the relation between those (X and Y) is positive, so they are positively correlated.
What is difference between covariance and variance?
Covariance: An Overview. Variance refers to the spread of a data set around its mean value, while a covariance refers to the measure of the directional relationship between two random variables.
What is a variance covariance matrix?
Briefly, the variance for a variable is a measure of the dispersion or spread of scores. Covariance indicates how two variables vary together. The variance-covariance matrix is a compact way to present data for your variables. The variance is presented on the diagonal (where the column and row intersect for the same variable), while the covariances reside above or below the diagonal.
Why is covariance important?
Covariance is important because it measures the relationship between two variables. It indicates the direction and strength of the relationship between the variables. Covariance can help in understanding and predicting the behavior of variables and is widely used in statistics, finance, and economics.
What is co-variance?
Covariance is a measure of how much two variables change together.If one variable changes how much will the other change?Example people's length and weight change together (within certain limits) taller people are in general heavier than shorter people. These two variables have great covariance.Whereas eye color has little relationship to height. those two variables have small (or no) covariance.
What is analysis of covariance used for?
Analysis of covariance is used to test the main and interaction effects of categorical variables on a continuous dependent variable, controlling for the effects of selected other continuous variables, which co-vary with the dependent. The control variables are called the "covariates."
What is the difference between correlation and covariance?
Correlation is scaled to be between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless. The covariance however, ranges from zero, in the case of two independent variables, to Var(X), in the case where the two sets of data are equal. The units of COV(X,Y) are the units of X times the units of Y. correlation is the expected value of two random variables (E[XY]),whereas covariance is expected value of variations of two random variable from their expected values,
What is the method used to demonstrate a cause and effect relationship between two variables?
Statistically, you would need to conduct an experiment in which every single other variable was controlled. Not a feasible option so you control the obvious covariates and examine the residual covariance between the two variables of interest. Even so, you may not find something. For example, the covariance between x and y where y= x2 over any symmetric interval is 0.
Will the variance of the difference of two independent normally distributed random variables be equal to the SUM of the variances of the two distributions?
Yes it is. That is actually true for all random vars, assuming the covariance of the two random vars is zero (they are uncorrelated).
Where can one find information on the covariance matrix?
One can find information on the covariance matrix on the Wikipedia website where there is much information about the mathematics involved. One can also find information on Mathworks.
When do you use an F test?
When testing the sums of squares of variables which are independently identically distributed as normal variables. One of the main uses of the F-test is for testing for the significance of the Analysis of Variance (ANOVA) or of covariance.
Find the formula for percentage of covariance?
100 x (standard deviation/mean)
