Regression analysis of the initial model

It was decided to fit the model expressed by Equation 10.6 to the most recent 100 data points only (i.e., starting with sequence number 72) and then use the earlier data points to test the predictive capability of the fitted model (although the prediction is backward in time see Section 3.5 and Exercise 4.19). Table 10.2 lists the parameter estimates and levels of confidence. Table 10.3 gives the ANOVA table and other statistics for the fitted model. 

The offset parameter (P = 7.072 at the 100.(KX)% level of confidence) does not represent an average response, but rather corresponds to the clearings at day zero when all of the other factor effects have been removed. It represents a reference point to which the factor effects can be added. 

The second parameter (P = 1.585 at the 99.895% level of confidence) is the hypothesized monthly cyclical term. The high level of significance indicates that it is extremely unlikely (a = 0.00105) that the correlation of the data with this cycle is accidental it is more likely that the cyclical effect of time is real. 

Finally, as expected, the day-of-the-week effect is negative and relatively large (Pj = -1.206 at the 100.000% level of confidence). 

Note that the Fisher F-ratio for the significance of lack of fit cannot be tested because there are no degrees of freedom for purely experimental uncertainty. This lack of degrees of freedom for replication is a usual feature of observational data. Any information about lack of fit must be obtained from patterns in the residuals. 

---