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In statisticssimple regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) 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.

Another definition is that it is a method for determining an optimal equation (least-squared difference between observed and predicted values for the response) for a response as a function of just one input variable: Y= b0 + b1 X + error. In other words simple regression is the relation between selected values of x and observed values of y (from which the most probable value of y can be predicted for any value of x).

#### References

Wikipedia. Simple Linear Regression. https://en.wikipedia.org/wiki/Simple_linear_regression