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In this video I will expand the previous videos&nbsp;
principle to covariance matrixes. So a correlation&nbsp;&nbsp;

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matrix is the special case of covariance matrix&nbsp;
that has been scaled so that the variance of its&nbsp;&nbsp;

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variable is 1. So core correlation matrix is kind&nbsp;
of like a standardized version of a covariance&nbsp;&nbsp;

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matrix. Some features of linear models are&nbsp;
better understood in covariance metric,&nbsp;&nbsp;

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so understanding the same set of rules in&nbsp;
covariance form is useful. Let's take a look at&nbsp;&nbsp;

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the covariance between X 1 and Y. We calculate&nbsp;
the covariance X 1 y exactly the same way as&nbsp;&nbsp;

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we calculated correlation. So we take there are&nbsp;
the unstandardized regression coefficients here,&nbsp;&nbsp;

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so previous will be working with standardized&nbsp;
regression coefficients, these are now on&nbsp;&nbsp;

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standardized because we are working on the raw&nbsp;
metric instead of the correlation matrix. So we&nbsp;&nbsp;

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have X 1 to Y 1 path. We get the beta 1 goes&nbsp;
here. Then another way of X 1 to Y is to our&nbsp;&nbsp;

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travel 1 correlation a covariance X 1 to X 2 so&nbsp;
that's covariance and then ricca-san path. So&nbsp;&nbsp;

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we get that and then our X 1 2 X 3 1 covariance&nbsp;
and then 2 y so that's all there are after we sum&nbsp;&nbsp;

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those together. That gives us the covariance&nbsp;
between X 1 and Y and that's exactly the same&nbsp;&nbsp;

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math than we had in a correlation example but&nbsp;
instead of working with correlations we work&nbsp;&nbsp;

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with covariances. Things get more interesting&nbsp;
when we look at what is the variance of Y. So&nbsp;&nbsp;

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the variance of Y is given by that equation&nbsp;
here. So the idea is that on we go from Y,&nbsp;&nbsp;

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and then we go to each source of variance of Y&nbsp;
and then we come back. So we go from Y to X 1,&nbsp;&nbsp;

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we take the variance of X 1 and then we come back.&nbsp;
So its variance of X 1 times beta 1 squared in the&nbsp;&nbsp;

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correlation matrix we just take beta 1 and beta&nbsp;
1 squared because the variance in correlation&nbsp;&nbsp;

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matrix is one so we just ignore that. When&nbsp;
we go from Y to R to X 1 X 2 and X and beta&nbsp;&nbsp;

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2 then we get that here and we go it both ways.&nbsp;
So why that are this is a useful rule is because&nbsp;&nbsp;

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it allows us to see that the variance of Y is a&nbsp;
sum of all these different sources of variation,&nbsp;&nbsp;

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so we get variation due to X covariance due to X 1&nbsp;
X 2 we get variation due to the error term. So the&nbsp;&nbsp;

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variation of Y is the sum of all these variances&nbsp;
and covariances of the explanatory variables,&nbsp;&nbsp;

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plus the variance of U the error term that is&nbsp;
our uncorrelated all the explanatory variables.&nbsp;&nbsp;

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This covariance form of the model employed&nbsp;
a correlation matrix rule is useful when&nbsp;&nbsp;

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you start working more complicated models,&nbsp;
such as confront a factor analysis model.