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. **After
**QuadReg** appears alone on the screen, 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.

**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**
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.

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.

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