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What Is a Line of Best Fit?

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  • Written By: Richard Nelson
  • Edited By: John Allen
  • Last Modified Date: 22 November 2016
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    Conjecture Corporation
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In math, the line of best fit is a line that can be drawn relating the points in a scatter plot of data. Scatter plots are made when two properties of something are related, like the day and high temperature for the day. The line of best fit best describes the points on a scatter plot when the average difference between where the line is drawn and the closest point is the least. This is easy to check with the least square method. Equations are sometimes used to describe the lines as a function when only one point will relate to a point on the line of best fit.

It is important to understand that all lines have a slope and an intercept. The slope describes how fast the line changes between any two relationships. The intercept describes a point when part of the relationship will become zero if the line was extended to that point.

Developing a good fitting line is useful because it allows predictions to be made when data is not presented. If only two points are plotted only one line can be drawn with a ruler as a straight line between the two points. With only two points, the line of best fit is exact and does not need to be checked. It can now display the exact position of a relationship that would land between the two points.

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A scatter plot of two relationships is how most data is recorded in statistics. Most scatter plots have many points, and using a ruler to draw a line of best fit is no longer the proper technique. If the relationship is considered first ordered then the line of best fit will still be a straight line but this line does not have to touch any points.

The least square method will determine whether one line will fit the data better than another. It does this by seeing if the difference between each plotted point and the point the line predicts is the smallest difference possible. Averaging the differences provides a number that represents how well the line fits the data. Other lines might get a lower value and become the new line of best fit in a process called linear regression.

Not every line is a straight line, many are curves and even three-dimensional. Multiple linear regression is the statistical technique used to find a line of best fit for data that does not follow a straight line. Regression refers to curve and surface fitting, but even for these much tougher uses of the line of best fit, the least square method is still used to check and compare results.

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