Slope and Intercept

Regression Analysis

Regression analysis is the process of building a model of the relationship between variables in the form of mathematical equations. The general purpose is to explain how one variable, the dependent variable, is systematically related to the values of one or more independent variables. An independent variable is so called because we imagine its value varying freely across its range, while the dependent variable is dependent upon the values taken by the independent. The mathematical function is expressed in terms of a number of parameters that are the coefficients of the equation, and the values of the independent variable. The coefficients are numeric constants by which variable values in the equation are multiplied or which are added to a variable value to determine the unknown. A simple example is the equation for the regression line which follows:

$y=mx+b$

Here, by convention, $x$ and $y$ are the variables of interest in our data, with $y$ the unknown or dependent variable and $x$ the known or independent variable. The constant $$$m$ is slope of the line and $b$ is the $y$-intercept -- the value where the line cross the $y$ axis. So, $m$ and $b$ are the coefficients of the equation.

Linear regression is an approach to modeling the relationship between a scalar dependent variable $y$ and one or more explanatory (independent) variables denoted $X$. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, it is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable).