## Cubic Regression

The cubic regression option finds the equation of a cubic equation of the
form y = ax^{3} + bx^{2} + cx + d that best fits a set
of data. First, enter
the data . Press .

Press
and use
to select CALC.

Press .

Therefore, the best-fit cubic equation for this data is approximately
y = 0.43x^{3} - 0.42x^{2} -1.1x -5.1. The TI-83 stores
the regression equation. The equation can be graphed and is transfered
to
without typing the equation as follows. Press
and use
to select EQ.

Press
to view the regression equation and press .
The equation is now entered in .
Press .
The data points can also be viewed. Access STAT PLOTS by pressing
to turn the plots on. Press .

**Note:** The resulting cubic equation is an exact fit if four noncollinear, nonparabolic
data points are entered.
The TI-83 does not calculate the correlation coefficient r but does
calculate the coefficient of determination r^{2}. The value of
.999 indicates a very good fit.