Topic: Cubic Regression


Cubic Regression is a process by which the cubic (third degree) equation of "best fit" is found for a set of data.  Consider the data set below:

x -3 -2 -1 0 1 2 3
y 3 -8 -7 0 7 8 -3


Before performing the cubic regression, first set an appropriate viewing rectangle.   For this example, use the Viewing Rectangle:  [-4, 4,1] by [-10, 10, 1] so that all the data points will be clearly visible on the calculator screen.  Then make a scatterplot of the data values.  The Viewing Rectangle and scatterplot are shown below:

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator

To find the Cubic Regression, press STAT, then RIGHT ARROW to CALC.  Now select 6:CubicReg.   After CubicReg appears alone on the screen, press ENTER.  The cubic regression function will appear on the screen.

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator
Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator


As can be seen above, the cubic of best fit is given when a = -1, b = 0, c = 8, and d = 0 .  Since the form of a cubic equation is given by
, substituting the values for a, b, c, and d gives .

To visually inspect the results, enter the cubic regression equation in while leaving PLOT1 on for the data values.  Then press GRAPH to see how well the curve fits the data points. 

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator

Copying the Regression Equation Directly into Y Values

NOTE: The regression results may be copied by the TI83 calculator directly into the Y sub 1 for graphing purposes by using the following procedure: 

After the data values have been entered, press STAT, then RIGHT ARROW to CALC.  Now select 6:CubicReg.  

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator

After CubicReg appears alone on the screen, press VARS, then ARROW RIGHT to Y-VARS, noting 1:Function is selected.  Press ENTER to accept and note that 1:Y sub 1 is already selected.  Press ENTER to accept, then  press ENTER to calculate.   The result appears on the screen to several decimal places. 

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator
Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator

Now press to see that the equation has already been entered for Y sub 1 and is ready to graph.

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator

This is the preferred method for entering the regression equation into Y sub 1 , since rounding the values can introduce significant rounding errors.



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