In this lesson, students will learn how to represent the ways in which two data sets are related.
One of the goals of using the correlation coefficient is to determine if and how closely two variables are related. The two simplest ways in which two variables can be related is that as one of them increases the other increases, or if one increases, the other decreases.
A scatterplot, has two axes, the horizontal and the vertical.
The horizontal axis is called the x-axis. The values presented along this axis are the x values of the points given in the scatterplot. The vertical axis is called the y-axis. The values presented along this axis are called the y values of the points given in the scatterplot.
If the data in a scatterplot closely follows a straight line, it is important to be able to describe how one variable changes due to changes in another variable. Being able to describe this relationship gives us some insight regarding the prediction of trends in the data. In the event that the data is generally spread out, our prediction will not be accurate, but if the data is clustered closely, our prediction could be plausible.
The steepness of the line is explained by what is known as the line slope. If the slope of a line is positive, the line rises from left to right.
If the slope is negative, the line falls from left to right.
Recall from previous lessons that there are independent and dependent variables. The slope of a line describes how much the y variable, or the dependent variable, changes if the x variable, which is the independent variable, increases. If the slope is positive, the y variable increases as the x variable increases. If the slope is negative, on the other hand, the y variable decreases as the x variable increases.
Take a look at an example here of annual income of an individual and the value of their home:
The line that you see is the line of best fit based upon the observations on the scatterplot, and the slope is positive.
Now take a look at a scatterplot that illustrates the amount of time an individual spends exercising per day and their body fat percentage.
Notice that there’s a downward-sloping line. This makes sense because the more somebody exercises, the lower the level of body fat they usually have. That’s not necessarily the only thing that could reduce body fat, but it does make sense that there would be a relationship here.
Source: This work is adapted from Sophia author Dan Laub.
How much the y-variable changes if the x-variable increases.