Regression analysis with its types, objectives and applications

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Regression analysis is a statistical technique that develop a relationship between explanatory (independent) variable and response (dependent) variable. It measures the dependence of one (dependent) variable on one or more than one other (independent) variable.

Linear regression

Introduction of regression analysis

The term regression was first introduced in nineteenth century to describe a biological phenomena, namely that the progeny of exceptional individuals tends on average to be less exceptional than their parents and more alike their more distant ancestors. Francis Galton, cousin of Charles Darwin studied this phenomena. He said that the mean value of a child’s characteristic (such as height, weight etc) was not equal to his /her parents height/weight but rather was between this value and the average value of the entire population. Thus, for instance , the height of the offspring of very tall people (called by Galton, people “taller than mediocrity”) would tend to be shorter than their parents. Galton called this phenomenon ‘regression to mediocrity’.

Objectives of Regression analysis

Estimate the relationship between explanatory and response variable.
Determine the effect of each of the explanatory variables on the response variable.
Predict the value of the response variable for a given value of explanatory variable.

Types of regression analysis

There are various types of regression analysis based on the regression model. Such as,

Linear Regression
Logistic Regression
Polynomial Regression
Stepwise Regression
Ridge Regression
Lasso Regression
ElasticNet Regression

There are three types of linear regression , i.e

Linear regression model
Multiple linear regression model
Polynomial regression model

Linear regression model

A regression model where exist one dependent (response) variable and one independent (explanatory) variable.

Multiple linear regression model

A regression model where exist one dependent (response) variable and more than one independent (explanatory) variable.

Polynomial regression model

A regression model where exist one dependent (response) variable and one independent (explanatory) variable but there is a polynomial function exist in the explanatory variable..

Application of regression model

A company might wish to improve its marketing process. After collecting data on the demand for a product, the product’s price and the advertising expenditure incurred in promoting the product, the company might use regression analysis to develop an equation to predict the future demand on the basis of price and advertising.
A real state company fixes the selling price of its apartments, as it claims, on the basis of the size of the apartments measured in terms of square footage of living space. A sample of 20 apartments was chosen and the apartment owners were asked to report the size of their apartments and the price they paid. On basis of this information, a regression analysis may be undertaken to see if there is any basis of such claim of the company and to make prediction of the price for a specified floor space.
A physician collected blood sample from 50 infants on pulmonary blood flow (PBF) and pulmonary blood volume (PBV) to examine if there is any relationship between PBF and PBV. A linear regression analysis seems appropriate for purpose to see if there is any such relationship.

What is standard deviation in regression model?

This is common question that everybody asked about regression. In regression model the differences between the regression line and the data at each value of the independent variable is called standard deviation.
And more simply
standard deviation= Root of Mean Square Error(RMSE)