Residual Sum of Squares - Matrix Expression For The OLS Residual Sum of Squares

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:

    “The matrix is God?”
    “In a manner of speaking, although it would be more accurate ... to say that the matrix has a God, since this being’s omniscience and omnipotence are assumed to be limited to the matrix.”
    “If it has limits, it isn’t omnipotent.”
    “Exactly.... Cyberspace exists, insofar as it can be said to exist, by virtue of human agency.”
    William Gibson (b. 1948)

    When I hear the hypercritical quarreling about grammar and style, the position of the particles, etc., etc., stretching or contracting every speaker to certain rules of theirs ... I see that they forget that the first requisite and rule is that expression shall be vital and natural, as much as the voice of a brute or an interjection: first of all, mother tongue; and last of all, artificial or father tongue. Essentially your truest poetic sentence is as free and lawless as a lamb’s bleat.
    Henry David Thoreau (1817–1862)

    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 (1817–1862)

    the possibility of rule as the sum of rulelessness:
    Archie Randolph Ammons (b. 1926)

    And New York is the most beautiful city in the world? It is not far from it. No urban night is like the night there.... Squares after squares of flame, set up and cut into the aether. Here is our poetry, for we have pulled down the stars to our will.
    Ezra Pound (1885–1972)