To discuss the differences and similarities when finding a trend line and a line of best fit for a set of data pairs, lets first recall each of them and then draw our conclusions.
Drawing a Trend Line
A trend line is a line we draw on a scatter plot to show the correlation between points more clearly, and even to estimate values beyond our known data. We draw a line near the points, or maybe even using a specific pair of points if we want to do our predictions based on them.
In the graph shown above we can see two different trend lines for the data sets. Even though both of them represent the general relationship well, we can see that the green line fits best for the green points and the orange line fits better for the orange points.
Drawing a Line of Best Fit
When we look for a line of best fit, we want to find the line that best represents all of the data on the scatter plot. In other words, the line of best fit is a trend line that shows the relationship between the whole data sets more accurately. We can find it using a graphic calculator. It uses a process called linear regression that adjusts the line to the data, minimizing the error between them.
The graph shown above is the same one used before. This time, we can see that the line used does a better job at representing the whole data set than the trend lines we used before.
Conclusions
Similarities
Both trend lines and lines of best fit are used to show the overall relationship of two data sets in a scatter plot, allowing us to do estimations beyond our known data and see its behavior.
Differences
While the line of best fit is also a trend line, it is a special case. It is the specific trend line that best represent the whole data, considering all the points we have.
On the other hand, a trend line can be any guess of a line that is near the points we have, or maybe using just two of them.
