# In CFA, are the unstandardized regression weights equivalent to the covariance between a factor and a manifest variable?

Also, are the standardized regression weights equivalent to the correlation between a factor and a manifest variable?

I write this question with reference to an example on p138-142 of the following document: ftp://ftp.software.ibm.com/software/analytics/spss/documentation/amos/20.0/en/Manuals/IBM_SPSS_Amos_User_Guide.pdf.

Here are illustrative figures and a table:

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$$\beta = X^{-1}Y$$ Where X is the correlation matrix of the predictors (if we're doing everything standardized). If the predictors are uncorrelated, then $X^{-1}$ is an identity matrix, and so $\beta = Y$. Same with CFA, if your factors are uncorrelated, then regressions are correlations. If not, then they're not.