## 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 = -18.5 + 41.7 ln x. The TI-83 calculates the correlation coefficient,
r. In this case, r is about 0.899. 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. It also calculates the
value of the coefficient of determination, r^{2}.
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 TI-83 calculates the correlation coefficient r and the value of r^{2},
the coefficient of determination.