Business Analysis Module User’s Guide
:
Chapter 3 Definitions
:
Multiple Linear Regression
:
Parameter Calculation by Least Squares Minimization
Parameter Calculation by Least Squares Minimization
The
method of least squares
consists of minimizing
with respect to
β
. Setting
θ
= X
β
, we minimize:
subject to:
Let
be the least squares estimate of
β
. The fitted regression
is denoted by:
The elements of
are called the
residuals
. The value of:
is called the
residual sum of squares
. The matrix:
which is the regression matrix without the first column of 1s, is called the
predictor data matrix
.
Model Variance
The variance of the model is defined to be the variance of
ε
. The statistic:
is an unbiased estimator of this variance.