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Concept

Line of Best Fit

A line of best fit, also known as a regression line, is a line of fit whose equation has been determined using a strict mathematical method that estimates the relationship between the values of a data set.
Points and Line of Best Fit

One commonly used method to determine a line of best fit is the method of least squares. It should be noted that the methods used to find the line of best fit are usually hard to do by hand. Therefore, a line of best fit can be found by performing a linear regression on a graphing calculator. As an example, consider the data set graphed above.

x 0.6 1.2 2.6 3.6 4.5 6 6.6 7.1
y 1.5 3.6 5.2 6.3 8.7 10.3 11.8 11.7

In reference to the graph, the data points seemingly can nearly be generated by the line y=1.55x+1.14. Consequently, even if the data points do not belong to any particular line, a linear model can be said to describe the data well enough. On the contrary, consider the following data set.

x 0.6 1.2 2.6 3.6 4.5 6 6.6 7.1
y 1.5 8.1 9.5 12 7.1 2.5 11.6 1.5

Look at the data points graphed onto a coordinate plane.

Points withoud Line of Best Fit

Looking at the graph, it can be seen that the points are not close to any line. Therefore, the data set is not well described by a linear model. Any line of fit used to estimate a relationship between the values will not be useful.

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