## Logarithmic Regression

The logarithmic regression option finds the equation of a logarithmic equation of
the form y = a + b ln x that best fits a set of data.
First,
enter the data . Press
.

The values of x 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 y.)
Press and use
to select CALC.

Press .

Therefore, the best-fit logarithmic equation for this data is approximately
y = -1.61 + 3.76 ln x.
The TI-82 calculates the correlation coefficient, r. In this case, r is about 0.99.
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.