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I calculated the cubic regression for a set of numbers following the instructions on this site:

http://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=71235

I am wondering how do I evaluate using the equation provided by the cubic regression without having to write down the equation on paper, and then typing in in the calculator.

Ted

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On a TI-83/84 series calculator (also an Nspire with the TI-84 keyboard module in place), once you've performed the regression, go to your "y=" screen, to a blank equation, press the "vars" key, go down to "5: Statistics...", arrow right twice to "EQ", and press enter to select "RegEQ"—this will insert the full regression equation into the y-variable line you were on in the "y=" screen.

animated screenshot of the steps

Now, you can use the graph and trace to evaluate or use the table to evaluate (or directly evaluate on the home screen using $Y_1(value)$, but that's harder to use).

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This should answer your troubles on how to store the regression equation to an equation variable on the TI 83/84/+/SE calculators. Alternatively, the coefficients a-d are accessible from the [VARS] > Statistics… > EQ menu.