Linear Regression is a process by which the formula of a line of "best fit" is found for a set of data.  Consider the data set shown below:

x01235
y348910

Before finding the linear regression, first set an appropriate viewing rectangle.   For this example use the Viewing Rectangle  [-1, 6,1] by [0, 15, 1] so that all the data points will be clearly visible on the screen.  Then make a scatterplot of the data values.  The Viewing Rectangle and scatterplot are shown below:

Screen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator

To find the Linear Regression, press STAT, then RIGHT ARROW to CALC.  Select 4:LinReg(ax+b).   After LinReg(ax+b) appears alone on the screen, press ENTER.  Then the result will appear on the screen.

Screen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator
Screen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator

In the case of the sample data given here, the line of best fit is given when a =1.5, b =3.5.  Substituting a and b into the equation gives the result for the line best fitting the data set:  

To visually inspect the results, enter the equation in while leaving PLOT1 on.  Then press GRAPH to see how well the line fits the data points. 

Screen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator

Copying the Regression Equation Directly into Y Values

NOTE: The regression results may be copied directly into for graphing using the following procedure: 

After the data values have been entered, press STAT, then RIGHT ARROW to CALC.  Select 4:LinReg(ax+b).    

Screen Picture of TI-83 CalculatorScreen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator

To copy the regression equation directly into , after LinReg(ax+b) appears alone on the screen, press VARS, then ARROW RIGHT to Y-VARS, noting 1:Function is selected.  Press ENTER and note that 1: is already selected.  Press ENTER again.  Press ENTER to calculate.   The result appears on the screen. 

Screen Picture of TI-83 CalculatorScreen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator
Screen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator

Now press to see that the equation has been entered for . Press GRAPH and the line appears on the screen as shown below.

Screen Picture of TI-83 CalculatorScreen Picture of TI-83 Calculator

Show Me

This is the preferred method for entering the regression equation into since rounding the values can introduce significant rounding errors.



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