**Cubic Regression** is a process by which the cubic (third degree) equation of "best fit"
is found for a set of data. Consider the data set below:

x |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |

y |
3 |
-8 |
-7 |
0 |
7 |
8 |
-3 |

Before performing the cubic regression, first set an appropriate **viewing rectangle****.
**For this example, use the **Viewing Rectangle**:
[-4, 4,1] by [-10, 10, 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 find the **Cubic
Regression,** press **STAT, **then **RIGHT ARROW**
to **CALC.** Now select **6:CubicReg. **After
**CubicReg** appears alone on the screen, press **ENTER**.
The cubic regression function will appear on the screen.

As can be seen above, the cubic of best fit is given when

To visually inspect the results,
enter the cubic regression equation in
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 by the TI83 calculator directly into the for graphing purposes
by using the following procedure:

After the data values have been
entered, press **STAT, **then **RIGHT ARROW** to **CALC.**
Now select **6:CubicReg. **

After **CubicReg**
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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