## Simple Linear Regression

To describe the linear association between quantitative variables, a statistical procedure called regression often is used to construct a model. Regression is used to assess the contribution of one or more “explanatory” variables (called independent variables) to one “response” (or dependent) variable. It also can be used to predict the value of one variable based on the values of others. When there is only one independent variable and when the relationship can be expressed as a straight line, the procedure is called simple linear regression.

Any straight line in two‐dimensional space can be represented by this equation:

y = a + bx

where y is the variable on the vertical axis, x is the variable on the horizontal axis, a is the y‐value where the line crosses the vertical axis (often called the intercept), and b is the amount of change in y corresponding to a one‐unit increase in x (often called the slope). Figure 1 gives an example.

Figure 1. A straight line.