Simple linear regression

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, simple linear regression (SLR) is a <a href="/facts/Linear_regression/5n998IhK">linear regression</a> model with a single <a href="/facts/Covariate/dINfzIF2">explanatory variable</a>. That is, it concerns two-dimensional sample points with <a href="/facts/Dependent_and_independent_variables/dINfzIF2">one independent variable and one dependent variable</a> (conventionally, the x and y coordinates in a <a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian coordinate system</a>) and finds a linear function (a non-vertical <a href="/facts/Straight_line/gJqsr4Gj">straight line</a>) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable.
The adjective simple refers to the fact that the outcome variable is related to a single predictor.
It is common to make the additional stipulation that the <a href="/facts/Ordinary_least_squares/q7H9k5vM">ordinary least squares</a> (OLS) method should be used: the accuracy of each predicted value is measured by its squared <a href="/facts/Errors_and_residuals/Ef0LgAS4">residual</a> (vertical distance between the point of the data set and the fitted line), and the goal is to make the sum of these squared deviations as small as possible. 
In this case, the slope of the fitted line is equal to the <a href="/facts/Pearson_correlation_coefficient/Igf0xDPc">correlation</a> between y and x corrected by the ratio of standard deviations of these variables. The intercept of the fitted line is such that the line passes through the center of mass (x, y) of the data points.

Simple linear regression open-in-new

Simple linear regression