How to Define and Use the Simple Linear Regression Model

Let’s start with some dry theory. A linear regression model is a linear approximation of a causal relationship between two or more variables. Regressions models are highly valuable, as they are one of the most common ways to make inferences and predictions.


The process goes like this. You get sample data, come up with a model that explains the data, and then make predictions for the whole population based on the model you’ve developed.


There is a dependent variable, labeled Y, being predicted, and independent variables, labeled x1, x2, and so forth. These are the predictors. Y is a function of the X variables, and the regression model is a linear approximation of this function.


The easiest regression model is the simple linear regression: Y is equal to beta zero plus beta one times x plus epsilon.


Let’s see what these values mean. Y is the variable we are trying to predict and is called the dependent variable. X is an independent variable. When using regression analysis, we want to predict the value of Y, provided we have the value of X.