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, r2.

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 r2, the coefficient of determination.