## Power Regression

The power regression option finds the equation of an equation of
the form y = ax^{b} that best fits a set of data.
First,
enter the data . Press

The values of both x and y must be greater than zero. (This is because the method for
determining the values of a and b in the regression equation is a least-squares fit on
the values for ln x and ln y.)
Press and use
to select CALC.

Press
. (The exponential regression option can also
be obtained by using the
to select option B and pressing
.)

Therefore, the best-fit power equation for this data is approximately
y = 0.84x^{1.59}.
The TI-82 calculates the correlation coefficient, r. In this case, r is about 0.998.
The value of r lies between -1 and 1, inclusive. It is a measure of how well the
regression equation fits the data. A value of -1 or 1 indicates a perfect fit.
The TI-82 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 TI-82 calculates the correlation coefficient r.