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
to select CALC.
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, r2.
The TI-83 stores the regression equation. The equation can be graphed
and is transfered to
without typing the equation as follows. Press
to select EQ.
to view the regression equation and press .
The equation is now entered in .
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 r2,
the coefficient of determination.