If X is an n × k matrix of n observations on k “independent variables” and y an n × 1 vector of n observations on a single “dependent variable,” a least-squares estimate of the k × 1 coefficient vector b in the affine relation https://www.w3.org/1998/Math/MathML"> y = X b + e https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/math_166_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is defined as one that minimizes the sum of squares of the residuals, https://www.w3.org/1998/Math/MathML"> e ′ e = ( y = X b ) ′ ( y − X b ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/math_167_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>