#### Estimation

Estimation can be viewed as a process by
which the actual value of a variable is approximated (fitted)
by some procedure.

In order to estimate we use information
from a sample. The objective is to obtain an estimated value that
can approximate the value of a population parameter (that is not
known).

#### Point estimates

Typical point estimates are the sample mean
and the sample standard deviation. We view the estimation process,
then, as an approximation of a population value.

#### Interval estimation

This consists of finding an interval that
with high degree of probability will contain the true population
parameter.

#### Methods

There are several methods of estimation.
In point estimation we use the well known formulas of the sample
mean (average) and sample variance (an average of the square deviations
from the sample mean).

In regression the most widely used is least
squares, but there is also the method of maximum likelihood, and
others like minimum absolute deviation.

#### Least squares

The method of least squares is usually the
choice in the linear regression model. The objective here is to
either:

- estimate the necessary parameters to predict
the expected change, or
- predict the future values of the variable
to explain

The remainder of what is not explained by
the fitted value is a measure of the error of measurement. That
is,

ACTUAL = FITTED + ERROR
ACTUAL refers to the observed value of the
variable to be explained (for instance, sales of breakfast cereal)

FITTED refers to the predicted or measured
variation of the variable to be explained, and

ERROR refers to the difference (a residual)
between what is observed and what is measured.