# Regression

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## Definition: Regression

Regression in general is used to denote the method which attempt to fit a model to observed data so that the relationship between the two sets of variables can be quantified. Let us denote the two sets of variables as X, Y where our objective is to fit a model such that Y=f(X). Hence, the variations in Y can be examined by the variations in X and it is achieved through a common set of sample set containing X and Y.

Commonly, X and Y are expressed as independent and dependent variables in multiple linear regression and predictor and responses in general regression respectively. Here, regression is of two types: univariate- which uses only predictor and hence, doesn’t model the data well; multivariate- takes into account various variables at a time and hence, the modelling of data is even more accurate. Regression analysis is generally used in forecasting and also in various fuzzy logical schemes, learning rates etc.

The general form of each type of regression is:
Linear/univariate Regression: Y = a + bX + u
Multiple/multivariate Regression: Y = a + b1X1 + b2X2 + b3X3 +...+u
Where:
Y= the variable to be predicted; X= the independent variable; a= the intercept
b= the slope; u= the regression residual

For e.g.: in astronomical calculations, various light year measurements are made possible with the know distances of the planetary bodies in the universe. Then, regression is used to relate these distances and speed to arrive at the light years of an unknown body/trajectory. Here, it is advantageous to follow this method of modelling since it is practically impossible to calculate with all the various variables associated with it in an inexpensive and less-time consuming fashion. These models are based on the sample set taken into account and they precisely model the data. Linear regression, ordinary parametric regression, non parametric regressions are few of the various techniques for carrying out regression analysis.

Hence, this concludes the definition of Regression along with its overview.

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