Statisticians use models as a mathematical formula to describe the relationship between variables. Even with models, we never know the true relationship in practice. In this section, we will introduce the Simple Linear Regression (SLR) Model.
In simple linear regression, there is one quantitative response and one quantitative predictor variable, and we describe the relationship using a linear model. In the linear regression model view, we want to see what happens to the response variable when we change the predictor variable. If the value of the predictor variable increases, does the response tend to increase, decrease, or stay constant?
We use the slope to address whether or not there is a linear relationship between the two variables. If the average response variable does not change when we change the predictor variable, then the relationship is not a predictive one using a linear model. In other words, if the population slope is 0, then there is no linear relationship.
In this section, we present the model, hypotheses, and the assumptions for this test.