Matrix Expression For The OLS Residual Sum of Squares
The general regression model with n observations and k explanators, the first of which is a constant unit vector whose coefficient is the regression intercept, is
where y is an n × 1 vector of dependent variable observations, each column of the n × k matrix X is a vector of observations on one of the k explanators, is a k × 1 vector of true coefficients, and e is an n× 1 vector of the true underlying errors. The ordinary least squares estimator for is
The residual vector is, so the residual sum of squares is, after simplification,
Read more about this topic: Residual Sum Of Squares
Famous quotes containing the words matrix, expression, residual, sum and/or squares:
“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
—Margaret Atwood (b. 1939)
“All expression of truth does at length take this deep ethical form.”
—Henry David Thoreau (18171862)
“The volatile truth of our words should continually betray the inadequacy of the residual statement. Their truth is instantly translated; its literal monument alone remains.”
—Henry David Thoreau (18171862)
“We didnt come to dig in Egypt for medals. Much more is learned from studying bits of broken pottery than from all the sensational finds. Our job is to increase the sum of human knowledge of the past, not to satisfy our own curiosity.”
—John L. Balderston (18991954)
“An afternoon of nurses and rumours;
The provinces of his body revolted,
The squares of his mind were empty,
Silence invaded the suburbs,”
—W.H. (Wystan Hugh)