In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
12.
Using too small a value of the smoothing parameter is not desirable, however, since the regression function will eventually start to capture the random error in the data.
13.
This difference can be rewritten as the sum of two terms : the difference in expected risk between the sample and population iterations and that between the population iteration and the regression function:
14.
In addition, use is made of the correlation coefficient of all data ( Ra ), the coefficient of determination or coefficient of explanation, confidence intervals of the regression functions, and Anova analysis.
15.
The importance of being able to model the variance as a function of the mean lies in improved inference ( in a parametric setting ), and estimation of the regression function in general, for any setting.
16.
As in regular least squares, the goal is to estimate the unknown parameters in the regression function by finding values for parameter estimates that minimize the sum of the squared deviations between the observed responses and the functional portion of the model.
