Let's say we have one latent factor L and three observed variables X1, X2 and X3. From the variance/covariance matrix of X1, X2, X3, we create this latent factor that explains the most out of the communalities between the X variables. So we compute the loading of each variable to the factor (three coefficients estimated). Then we estimate the variances of each variable (as I have read in other places, the error variance in the case of the X variables).

The main question is:

• Why must we estimate (i.e. calculate or approximate an unknown) the variance of observed variables? We already have their variances in the original var-cov matrix and as far as I understand we have not modified the input data (i.e. we have only added variables into the equation, but not modified the variables we started with).

And the secondary questions (which most probably will be answered with the main answer) would be:

• If it is called the error variance, why do we expect the estimated variance to be close or equal to the original variance of the variables (as a mean of validating our model, as DataCamp suggests)? Shouldn't it be the original variance minus the variance explained by the factor?

I have not been able to find an answer to the following question (nor anyone else having the same question) so I assume that it has an evident answer that just escapes me.