## 7.2 SIMPLE REGRESSION MODELS

### 7.2.1 Overview

A simple regression model is a formula describing the relationship between one descriptor variable and one response variable. These formulas are easy to explain; however, the analysis is sensitive to any outliers in the data. The following section presents methods for generating simple linear regression models as well as simple nonlinear regression models.

### 7.2.2 Simple Linear Regression

#### Overview

Where there appears to be a linear relationship between two variables, a simple linear regression model can be generated. For example, Figure 7.9 shows the relationship between a descriptor variable **B** and a response variable **A**. The diagram shows a high degree of correlation between the two variables. As descriptor variable **B** increases, response variable **A** increases at the same rate. A straight line representing a model can be drawn through the center of the points. A model that would predict values along this line would provide a good model.

A straight line can be described using the formula:

*y = a + bx*

where *a* is the point of intersection with the *y*-axis and *b* is the slope of the line. This is shown graphically in Figure 7.10.

In Table 7.8, a data set of observations from a grocery store contains variables **Income** and **Monthly sales**. The variable **Income** refers to the yearly income for a customer and the **Monthly sales** represent the amount that particular customer purchases per month. This data can be plotted on a scatterplot and a linear relationship ...