Quadratic Regression is a process by which the equation of a parabola of "best fit" is found for a set of data.  Consider the data set shown below:.

x -1 0 1 2 3 4
y 6 -1 -3 -1.5 5 10

Before performing the quadratic regression, first set an appropriate viewing rectangle.   For this example use the Viewing Rectangle:  [-2, 5,1] by [-4, 11, 1] so that all the data points will be clearly visible on the calculator screen.  Then make a scatterplot of the data values.  The Viewing Rectangle and scatterplot are shown below:

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

To calculate the Quadratic Regression, press STAT, then RIGHT ARROW to CALC.  Now select 5:QuadReg.   After QuadReg appears alone on the screen, press ENTER.  Then the quadratic regression will appear on the screen.

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

As can be seen above, the parabola of best fit (to two decimal places) is given when a =1.68, b = -3.91, and c = -0.23.  The form of a quadratic equation is given by . Substituting the values for a, b, and c into this form gives the equation for the quadratic function best fitting the data set:

To visually inspect the results, enter the quadratic regression equation in Y= while leaving PLOT1 on for the data values.  Then press GRAPH to see how well the curve fits the data points. 

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

Copying the Regression Equation Directly into Y Values

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

After the data values have been entered, press STAT, then RIGHT ARROW to CALC.  Now select 5:QuadReg.  

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

After QuadReg appears alone on the screen, press VARS, then ARROW RIGHT to Y-VARS, noting 1:Function is selected.  Press ENTER to accept and note that 1: is already selected.  Press ENTER to accept, then  press ENTER to calculate.   The result appears on the screen to several decimal places. 

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

Now press to see that the equation has already been entered for and is ready to graph.

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

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



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