Equation for a Line
While the correlation coefficient is useful for telling us whether two variables are correlated, it does not describe the nature of the relationship between the two variables. Often we know or strongly suspect that two variables are related; what we want to know is precisely how they are related. For example, it is not surprising that there is a positive relationship between an automobile's speed and its stopping time on dry pavement. What we want to know is how much stopping distance increases with each speed increase of, say, 10 mph. Lines are very useful for describing relationships between two variables. Some relationships are much more complicated than lines, but lines always are a useful starting point and are often all we need for many relationships. Before we see how lines are used to model relationships between variables, we will first review the basis of lines and how they work. If you remember from an algebra or geometry course how lines work, you may skip ahead to estimating slopes. However, a quick review is good for everyone. The equation for a line is: Y = a + bX Two variables are related by the two parameters in the equation: a is the intercept and b is the slope. Use the graph below to explore how these parameters affect the line.