Interpreting the slope of a regression line

In this section, we’ll focus on the significance of the slope of a regression line and how it informs our understanding of the relationship between variables. By studying the slope, we can derive meaningful insights from our regression models and make well-informed decisions. We’ll illustrate this concept through various examples, highlighting the practical implications of interpreting the slope.

Recall that the equation for a simple linear regression line is as follows:

y = a + bx

The slope, b, represents the average change in the dependent variable, y, for each one-unit increase in the independent variable, x. In other words, it tells us how y is expected to change as x changes.

Let’s explore some examples to better understand the interpretation of the slope.

Example 1: A fitness coach has developed a simple linear regression model to predict weight loss based on the number of calories burned during exercise...