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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.

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.