What's the significance of the squared cosine value of a variable in statistical construction?
The interaction of two variables can be represented geometrically (and this is a common way of visualising correlations through scatter graphs etc). This means that geometric principles apply to variable interactions. It is the case that covariance (and hence correlation, which is a normalised version of covariance) interact via a cosine rule (the combined variance of two variables is the sum of the squared variance of the two variables plus a cosine term that captures the common variation).
a very nice introduction is available at
https://www.johndcook.com/blog/2010/06/17/covariance-and-law-of-cosines/
The interaction of two variables can be represented geometrically (and this is a common way of visualising correlations through scatter graphs etc). This means that geometric principles apply to variable interactions. It is the case that covariance (and hence correlation, which is a normalised version of covariance) interact via a cosine rule (the combined variance of two variables is the sum of the squared variance of the two variables plus a cosine term that captures the common variation).
a very nice introduction is available at
https://www.johndcook.com/blog/2010/06/17/covariance-and-law-of-cosines/
Dr. James- You have nicely explained the cosign and correlation. The attachment is also good.
Regarding my question, can you agree with the following statement on the significance of squared cosine, for example in factor analysis?
Squared cosine helps to select the representation quality of a variable on an axis during rotation. When the squared cosine related to an axis is low, that particular position of the variable on the said axis is not the proper representation quality.
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