Simple linear regression

Simple linear regression is a linear regression in which there is only one covariate (predictor variable).

Simple linear regression is used in situations to evaluate the linear relationship between two variables. One example could be the relationship between muscle strength and lean body mass. Another way to put it is that simple linear regression is used to develop an equation by which we can predict or estimate a dependent variable given an independent variable.

The regression equation is given by

${\displaystyle Y=a+bX}$

Where ${\displaystyle Y}$ is the dependent variable, ${\displaystyle a}$ is the y intercept, ${\displaystyle b}$ is the gradient or slope of the line and ${\displaystyle X}$ is independent variable.

The linear relationship between the two variables (i.e. dependent and independent) can be measured using a correlation coefficient e.g. the Pearson product moment correlation coefficient.

${\displaystyle b=Sxy/Sxx}$