Linear graphs are a terrific way to see a trend when comparing any two factors. A line of best fit is the trendline that best fits the data set. In this lesson, we will see how the line of best fit helps to predict future events.
What Is a Line of Best Fit?
The line of best fit , also called a trendline or a linear regression, is a straight line that best illustrates the overall picture of what the collected data is showing. It helps us to see if there is a relationship or correlation between the two factors being studied. This trendline helps us to predict future events relating to the data being studied.
In this figure, the red line of best fit shows the general trend of a person’s height at certain ages. As you can see, some of the points are on the line; some are above and some are below. This line helps us see the general trend of what is being studied. Let’s look at how the line of best fit can be calculated using Excel and then using the point-slope formula.
Excel and Line of Best Fit
Excel can help you easily calculate the line of best fit.
This example will show you how to use Excel to do this.
This information gives the values gathered to see if there is a relationship between student attendance percentages and final grades. The graph is set up using a Cartesian Coordinate System where the attendance percentage is on the x-axis and the final grades are on the y-axis.
So, for example, if a student went to class 90% of the time and that particular student earned an overall grade of 94%, we will graph this as 90 on the x-axis and 94 on the y-axis.
This is the scatter plot graph identifying these same students and includes a line of best fit, which was generated automatically by the Excel program. The Excel program allows you to easily graph the trendline.
As you can see, the linear equation:y = .6596x + 33.
12shows a positive slope and indicates that if a student attended zero times, they could possibly get a 33.12% as an overall grade.This trendline could also be used for other students to predict the grades they would receive. For instance, if Susie only wanted to come to class 80% of the time, she could expect to receive an 85% grade.
If a student wanted to earn a 90% or better, they would have to come to class about 90% of the time.
Point-Slope Formula and Line of Best Fit
While Excel easily calculates the line of best fit, you can also calculate a line of best fit by picking two data points and using the point-slope formula to generate the equation of the line. For instance, let’s choose two data points from this chart:
On this graph, you can see there are multiple trendlines that can be drawn on one set of data, but it is the line of best fit that generates the line that fits within all the data. The other lines are lines that fit just two data points.
Using the Line of Best Fit
A line of best fit allows us to predict the trends of what is being studied. For instance, if we wanted to know what types of salaries we would earn based on the number of years in college, we could gather the information needed and see our graph.
Using this table gathered from the Bureau of Labor Statistics, which shows income on the y-axis and years of college on the x-axis, we can see the income trends. Using the Excel program, we can create a scatter plot graph that shows there is an upward trend. The line of best fit indicates that the more a student attends college, the higher the salary.
The linear equation gives us a slope of $5,592.50 and a y-intercept of $33,607. The slope indicates that each year of college will increase the yearly salary by $5,592.50. As you can see, the line of best fit is situated within the center of the data points. It hits some points and misses others.
The line of best fit, trendline, or linear regression is the line that shows the general trend of relationship within the data scatter graph.
These trendlines can hit all the data or fall within the central location of the data. It allows one to make a prediction regarding the data.