#### 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:

1. estimate the necessary parameters to predict the expected change, or
2. 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.