Regression

Definition

Regression is a type of statistical analysis used for estimating the relationship between variables, Which explores the possible relationships between two or more variables, One variable called dependent variable or the response and another one is independent variable .

Regression helps us predict the value of the response variable with respect to the change in the independent variable , It estimates the conditional expectations of dependent variable given the independent variable.

Regression models

Regression has the following models

• 1        Linear regression
• 2.       Nonlinear regression
• 3.       More Complex regression called multiple regression which encompasses several independent variables).
• 4.       Logistic regression where the dependent variable is binary.

    Linear Regression

Simple Linear regression explores possible relationships among data of linear nature, where the relationship could be modeled as a straight line .

In general , a straight line could be modeled given the equation below

A = M * x + b

Where M is the slope of the regression line and b is the intercept which is the line crosses the y axis.

Conditions for linear regression to make it valid

A.      Normality : Regression is a parametric test, and assumes that the data are normally distributed.

B.      Linearity : A Linear relation exists between the dependent and the independent variables. Thus it is sensible to model the relationship as a straight line.

C.      Independence : That data should have been drawn independently.

D.      Unexplained variance : the portion of the variance of the dependent variable not explained by the independent variable is due to random error and follows a normal distribution.