Accuracy of Quadratic Regression

[Joe Horn]

(08-21-2023 05:52 PM)Albert Chan Wrote:  To get best fit coefficients, it may be better to reduce both x and y from its mean.
For your example, we can simply knock down year 2000, (2003 .. 2012) --> (3 .. 12)

(08-22-2023 06:35 AM)parisse Wrote:  2/ Accuracy can sometimes be improved, here by translating the data.

Most of the manuals for the older HP calculators explained this idea of "normalizing" data to avoid roundoff errors. For example, here's what the HP-32S manual says:

HP-32S Owner's Handbook Wrote:
Limitations on Precision of Data
Since the calculator uses finite precision (12 to 15 digits), it follows that there are limitations to calculations due to rounding.

Normalizing Close, Large Numbers.
The calculator might be unable to correctly calculate the standard deviation and linear regression for a variable whose data values differ by a relatively small amount. To avoid this, normalize the data by entering each value as the difference from one central value (such as the mean). For normalized x-values, this difference must then be added back to the calculation of x-bar and x-hat, and y-hat and b must also be adjusted. For example, if your x-values were 7776999, 7777000, and 7777001, you should enter the data as -1, 0, and 1; then add 7777000 back to x-bar and x-hat. For b, add back 7777000 × m. To calculate y-hat, be sure to supply an x-value that is less 7777000.

A cursory search did not find a similar explanation in the HP 50g or Prime owner's manuals.