Line Graphs vs Lines of Best Fit: What’s the difference?
8 great datasets to help - line - your curriculum with strong practices
The terms “line graph” and “graph with line of best fit” (or regression line) are sometimes mistakenly used by students in an interchangeable way. Because these graphs may initially look quite similar to our students, it can be very helpful to students to explicitly point out the differences. Being clear and direct as you define these graph types for students will help them to understand what the data in these two very different graph types are saying.
As an example, let’s look at the three graphs from the Classroom-Ready activity, Mass Extinctions. The graph on the left showing Extinction Rate over Age (Mya) is a line graph, while the other two graphs are graphs with two different types of lines of best fit, linear and quadratic.
Line Graph
Graph with Line of Best Fit
Graph with Curve of Best Fit
The Line Graph
In short, a line graph shows the data points directly connected point to point.
The line graph is a connection of data points (in a dot-to-dot fashion). It is an effective way to show fluctuation in your Y variable over time. Although the line graph is closely associated with presenting change over time data, it can also be used to show changes in Y that occur across a gradient of values on X, or show changes across categories that have a natural order.
Ways to make a bad line graph:
1) Data that has more than one observation of Y per each value of X. In cases like that, connecting the lines will make a messy graph where the line confuses the eye rather than clarifies.
2) Too much data and a line graph will make for a visual that is just a bit too busy to be interpreted well.
3) Inappropriate scaling (to large or too small). Too large a scale and all the fluctuations, which may be very important, will be hard to see, Too small a scale and all the fluctuations will appear deceptively large.
…This decrease in Electricity from coal from 1996 to 1997 looks huge when zoomed in like this. But when we look at the data as a whole, this year to year fluctuation looks far less important.
Want your students to get more practice with line graphs? Check out these activities for more:
Witches, Spider-Man, and Stranger Things in Data
When Whale I See You Again?
Mass Extinction: Past and Present
The Line of Best Fit
In short: A line of best fit shows a modeled relationship between X and Y.
The line of best is a model that gives a predicted value of Y for a given value of X. The regression line is calculated by minimizing the sum of the squared differences between each data point and the line. The line is always placed in the position that passes through the mean of X and the mean of Y AND minimizes the sum total of all of those squared differences. Because a line of best fit is a model of the relationship between X and Y it can be used to make predictions for Y based on a value of X that is not actually observed in the data. (This can not be done with a line graph). Note: A caution to this is that it may not be valid to make a prediction for Y based on a value of X that is completely outside of the range of values that were used to fit the line of best fit.
Want students to get more practice with lines of best fit? Check out these activities for more:
Linear fits:
The Plastics Problem
Struck Gold? A density investigation
Single Cell Survival of the Fittest
Curve of Best Fit
In short: A curve of best fit shows a modeled relationship between X and Y.
In algebra and beyond students will often encounter lines of best fit made with nonlinear functions such as quadratic or other functions. This fundamentally works the same way as the line of best fit from a linear regression. The curve will still minimize the sums of the squared differences between the data points and the line. However, the curve is not produced with a linear equation (y = mx + b), but rather it is produced with a quadratic equation (y = ax2 + bx + c) or other function.
Want students to get more practice with curves of best fit? Check out these activities for more:
Nonlinear fits: