To see why this is an issue, run Python in a shell session and perform this test: One student applied a data set of 97 x,y pairs and couldn't understand why the results became meaningless as he increased the polynomial degree (largest matrix exponent: 10 192). I've added this section after receiving a number of inquiries over the years from students who tried to get a classic perfect-match result by setting the polynomial degree to data points -1 with large data sets. This is not to say this method's results won't be usable for larger polynomial degrees, only that the classic result of perfect correlation for a degree equal to the number of data points -1 will be less likely to appear as an outcome. Thus, for some (but not all) data sets, as the polynomial degree increases past 7, the accuracy and usefulness of the results may decline in proportion. Larger polynomial degrees risk exceeding the resolution of the variables in use.
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