Linear regression in its generalized form

As discussed in Section 7.2, a multiple linear regression can be described by 

This equation can be written in a more generalised matrix form as follows  

The variance of the error is denoted by ar, and can be written using the variance, V  

In many experiments, the expected error is not constant for all observation points. We can stiU make a least squares minimization, but we cannot make any statistical analysis unless we stabilize the variance (see Section 7.4). For a detailed statistical analysis, each observation should be weighted with its variance. 

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