# Regression Analysis

### From MM*Stat International

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## The objectives of regression analysis

The main objective of regression analysis is to describe the expectation and dependence of a quantity on quantities . A one-directional dependence is assumed. This dependence can be expressed as a general regression function of the following form:
The symbol used indicates that the regression function of observed values is does not correspond to an observed value , but rather with the average value of given the ’s, which lies on the regression function.
**The random variables ** are referred as **regressors, explanatory variables** or **independent variables**.
**The random variable ** is referred as **regressand** or **dependent variable**.
An example is the simple linear regression with a dependent variable “Time working” and one independent variable “Amount of production.” Notice that this regression is referred to as simple because there is a single independent variable and is a linear regression since the function is assumed to be linear.

If the dependence of **Y** on **X** can be represented by a linear function, the regression value does describe the value of . It follows that the value of any observation can be decomposed as follows:
The difference between the observed values and the value of the regression function is called a residual . It contains those influences on that cannot be described by means of the regression function; alernatively, this means that deviations of the observed values from the regression function cannot be explained by the independent variables employed in the regression function.
**Regression function**
**The regression function is a representation of average statistical dependence of a dependent variable on one or more independent variables. The dependence is described by a function based on observations.**
In what follows, we assume only the case when a variable **Y** depends on a single variable **X**.
A form of the regression function **f(x)** always depends on the specific application and the purpose of an analysis.
Examples of possible regression functions include:

Linear function | |

Quadratic function | |

Power function | |

Exponential function | |

Logarithmic function |