# Linear Regression

**DOI:**https://doi.org/10.1007/978-1-4899-7993-3_542-2

## Definition

*Y*, explanatory variable or regressor

*X*= {

*x*

_{1}, … ,

*x*

_{ I }} and a random term

*ε*by fitting a linear function,

where *α* _{0} is the constant term, the *α* _{ i }s are the respective parameters of independent variable, and *I* is the number of parameters to be estimated in the linear regression.

## Key Points

Linear regression analysis is an important component for several tasks such as clustering, time series analysis, and information retrieval. For instance, it is a very powerful forecasting method for time series data. It helps identify the long-term movement of a certain data set based on given information and explore the dependent variable as function of time.

To solve the linear regression problem, there are various kinds of approaches available to determine suitable regression coefficients [1 *,* 2]. They include: (i) least-squares analysis, (ii) assessing the least-squares model, (iii) modifications of least-squares analysis, and (iiii) polynomial fitting. The primary objective is to select a straight line which minimizes the error between the real data and the line estimated to provide a best fit.

## Cross-References

### Recommended Reading

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## References

- 1.Draper, N.R., Smith, H. Applied regression analysis Wiley Series in Probability and Statistics; 1998.Google Scholar
- 2.Gross J. Linear regression. Berlin: Springer; 2003.Google Scholar