clearly show the difference between SRF and PRF graphically and also mention the difference between error and residual.how same graph would be helpful to understand the concept of R^2?
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misconception, surprisingly also in the replies above, to think that residuals are sample realizations of errors. This is *NOT* true.
In the classical multiple regression framework
Y = X*Beta + eps
where X is the matrix of predictors and eps is the vector of the errors
the assumption on the errors is that they have variance-covariance matrix
V[eps] = sigma^2 * I
where I is the identity matrix. This implies that residuals (denoted with res) have variance-covariance matrix:
V[res] = sigma^2 * (I - H)
where H is the projection matrix X*(X'*X)^(-1)*X'.
Hence, even if the inspection of the residuals helps diagnosing the assumptions on the errors, residuals and errors are different quantities and should not be confused.
HTH
Simone
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