e first row is an identity vector used for the intercept parameter

܆ൌ൬¹

1

⋯

1

ݔଵ

ݔଶ

⋯

ݔே^൰

(4.12)

LSE estimation of model parameters is shown below, where

is called the pseudo inverse,

ܟෝൌሺ܆^࢚܆ሻ^ି૚܆^࢚ܡ

(4.13)

n estimated weight vector ܟෝ, the final regression model is written

ܡො = ܆ ܟෝൌ܆ሺ܆^࢚܆ሻ^ି૚܆^࢚ܡ

(4.14)

that y and have different meanings. The former is a vector of

ܡො

vations and the latter is a vector of the regressed means or the

predictions) of a regression model. This can be easily extended to

ltivariate OLR models. In addition to LSE for estimating the

arameters for a regression model, other approaches such as the

approach [Box and Tiao, 1973] can also be used to estimate

n model parameters.

ess the fitness of a regression model

ression model, the first question is whether a regression model

a well. The measurement is called the fitness and it is related with

ssion errors. To show its importance and usefulness to assess a

n model, two regression models are shown in Figure 4.6. The

error was 0.0102 for the model shown in Figure 4.6(a) and was

r the model shown in Figure 4.6(b). Therefore they had different

f fitness. It is no doubt that the regression model shown in Figure

s a better fitness because it has a smaller error than the regression

own in Figure 4.6(b).