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.