## Linear Regression

The linear regression option finds the equation of a linear equation of
the form y = ax + b or y = a + bx that best fits a set of data. First,
enter
the data . Press .

Press
and use
to select CALC. Press
This yields an equation of the form y = ax + b.

The linear regression option can also be obtained by pressing .
This yields an equation of the form y = a + bx.

The resulting equations are equivalent, y = 0.24x + 1.14 and y = 1.14
+ 0.24x. The TI-83 calculates the correlation coefficient, r. In this case,
r is about 0.91. 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 .
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 resulting linear equation is an exact fit if two nonvertical data points are entered.
The TI-83 calculates the correlation coefficient r and the value of
r^{2}, the coefficient of determination.