The line of best fit is a mathematical tool used to describe the relationship between two properties in a scatterplot. It is determined by finding the line with the smallest mean difference between the line and the closest point. The slope and intercept of the line are important in describing the relationship. The least squares method is used to determine the best fit line, and it can be used for curved and three-dimensional lines as well.
In mathematics, the line of best fit is a line that can be drawn by relating points in a scatterplot of data. Scatterplots are created when two properties of something are related, such as day and high temperature for the day. The line of best fit best describes points on a scatterplot when the mean difference between where the line is drawn and the closest point is smallest. This is easy to verify with the least squares method. Equations are sometimes used to describe lines as a function when only one point will refer to a point on the best-fit line.
It is important to understand that all lines have a slope and an intercept. Slope describes how fast the line changes between two relationships. The intercept describes a point where part of the relation will become zero if the line has been extended to that point.
Developing a good line of fit is helpful because it allows you to make predictions when data is not presented. If only two points are drawn, only one line can be drawn with a ruler as a straight line between the two points. With only two points, the best fit line is exact and does not need to be checked. It can now visualize the exact location of a relationship that would land between the two points.
A scatterplot 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 correct technique. If the relationship is considered first ordered, the best fit line will still be a straight line, but this line must not touch any points.
The least squares method will determine if one row fits the data better than another. It does this by seeing if the difference between each plotted point and the point predicted by the line is the smallest possible difference. The mean of the differences gives a number that represents how well the line fits the data. Other lines might get a lower value and become the new best-fit line in a process called linear regression.
Not all lines are straight, many are curved 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 fit, but even for these much more difficult uses of the line of best fit, the method of least squares is still used to check and compare the results.
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