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:

To calculate the Quadratic Regression, press STAT, then RIGHT ARROW to CALC.  Now select 5:QuadReg. Arrow down to Calculate and press ENTER.  Then the quadratic regression will appear on the screen.

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.

## 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.

After QuadReg screen appears arrow down to Store RegEQ, then 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.

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

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