## Quartic Regression

The quartic regression option finds the equation of a fourth degree polynomial
of the form

y = ax^{4} + bx^{3} + cx^{2} + dx + e

that best fits a set of data.
First, press
to
enter the data .

The data shown here is the points {(2,11.4) (3,17) (5,27.3) (7,36.1) (11,47.7) (13,49.9)}.
To view the statistics calculation options press
.

Press find the quartic regression optiion -- polynomial of degree four, P4Reg.

Select P4Reg, .

Run quartic regression by pressing
. Scroll to the right to see all of the coefficients.

Therefore, the best-fit quartic equation for this data is approximately
y = .00011x^{4} - .0104x^{3} - .0504x^{2} + 6.037x - 3.89.
(Note the scientific notation for the first term.)

**Note:** The resulting quartic equation is an exact fit if five non-collinear, non-parabolic,
non-cubic data points are entered.
The TI-86 does not calculate the correlation coefficient r.