Fit Analyses |

If the errors do not have a common variance in the regression model

In parametric regression, the linear model is given by

Let **W** be an *n*×*n* diagonal matrix consisting of weights *w _{1}*>0,

The weighted fit analysis is equivalent to the usual (unweighted) fit analysis of the transformed model

The estimate of is then given by

**b**_{w}= (**X**'**W****X**)^{-1}**X**'**W****y**

For nonparametric weighted regression, the minimizing criterion in spline estimation is given by

In kernel estimation, individual weights are

For generalized linear models, the function for binomial distribution with *m*_{i} trials in the *i*th observation, for other distributions. The function is used to compute the likelihood function and the diagonal matrices **W**_{o} and **W**_{e}.

The individual deviance contribution *d*_{i} is obtained by multiplying the weight *w*_{i} by the unweighted deviance contribution. The deviance is the sum of these weighted deviance contributions.

The Pearson statistic is

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