Digital tools

Finding a Line of Best Fit

Most graphing calculators have a function called linear regression, which can be used to find a precise line of fit using strict rules. This line of fit is then called the line of best fit. For example, consider the following data set.

$x$	$y$
$1$	$33.12$
$2$	$24.4$
$3$	$16.6$
$4$	$9.3$
$5$	$3.9$

The line of best fit can be calculated following these $3$ steps.

Enter Values

On a graphing calculator, begin by entering the data points. To do so, press the $STAT$ button and select the option Edit.

The window in the calculator, which shows Stat and then Edit

This gives a number of columns, labeled $L_{1},$ $L_{2},$ $L_{3},$ and so on.

Use the arrow keys to choose where in the lists to fill in the data values. Enter the $x -$ values of the data points in $L_{1}$ and press $ENTER$ after each value. The same can be done for the the corresponding $y -$ values in column $L_{2} .$

Calculator that shows two lists where you entered values

Fitting the Line

After entering the values, press the $STAT$ button and select the menu item Calc.

Counter that displays the list of CALC and where you have chosen LinReg

The option LinReg(ax+b) gives the line of best fit, expressed as a linear function in slope-intercept form. Press the $ENTER$ button until the parameters are given.

Calculator showing a linear function regression

In this case, the line of best fit is described by the function $y = - 7.354 x + 39.506 .$ The correlation coefficient $r$ is less than $- 0.99,$ indicating a strong negative correlation. If $r$ does not appear, press $2ND$ and $0$ to get to the CATALOG, then select DiagnosticOn and enable it by pressing $ENTER$ twice. Once more, find the line of best fit.

Graphing the Line of Best Fit

A graphing calculator can also be used to graph the line of best fit. After selecting the option LinReg(ax+b), choose the option Store RegEQ.

Press $VARS$ and move to the Y-VARS menu. Then, select the option FUNCTION and press $ENTER .$

Press the $ENTER$ button until the parameters are given. To graph the scatter plot, first push the buttons $2nd$ and $Y = .$ Then, choose one of the plots in the list. Select the option ON, choose the type to be a scatter plot, and assign $L_{1}$ and $L_{2}$ as XList and Ylist, respectively.

Then, the plot can be made by pressing the button $GRAPH .$ It is possible that after drawing the plot the window-size is not large enough to see all of the information.

To fix this, press $ZOOM$ and select the option ZoomStat. After doing that, the window will resize to show the important information.

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