g

s, the less the chance for data to occur. In other words, there is

ess chance for the data to be very far away from zero. Therefore,

aped density curve can be seen. Having had this data set, the

of a regression analysis is to find a proper way to regress the

ons to their mean, i.e., zero for this case.

he true value is the mean of a data set, where it is assumed that the data follow

distribution. ߪ stands for one standard deviation. A rug at the bottom of the

s the spectrum of the observed data.

having a number of the regressed means may not be of great

In fact, if these regressed means are interpolated, a continuous

n function can be generated. This is what the magic regression

can do. An example is shown in Figure 4.2. Based on the observed

ch were the filled dots in the plot and treated as the corrupted

ons, a regression process was used to find their true values, which

d as the regressed means. Based on the regressed means, an

tion process is used to generate a regressed mean (regression)

The regressed (regression) function is continuous in most

n analysis models. The most important feature of a continuous

n function is its capability for the inference on novel data.

ression model can be either linear or nonlinear depending on a

and depending on how a question is examined. Both have the

and the limitations. A linear regression model enjoys the

nt benefits of the excellent interpretation capability and the

extrapolation capability. However, when a question becomes

ted, a linear regression model may lose its advantage, becoming

to explain the relationship between variables. In this situation, a