In class, we would run power regression for sets of data points to find variation equations. The power regression takes a set of points and fits it to the model $$\hat{y}=ax^b $$

When doing it on the calculator (TI 89 Titanium if that matters) after it does the regression, it lists two more sets of values into the table: residt and resid.

I am familiar with what the "resid" represents: the residuals, or the error between predicted and actual y-values.

However, I am not sure what the "residt" could represent. One thought was that it may have been standardized residuals, but then I noticed it doesn't show up whenever I do a simple linear regression, so I am not so sure.

Thanks for any help or clarification given

  • $\begingroup$ They are probably "studentized" residuals since Student (Gosset) was known for his "T" distribution. $\endgroup$ – AdamO Mar 8 '18 at 17:25
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    $\begingroup$ @AdamO No. Searching the TI-89 manual, "Residuals associated with the linear fit of the transformed data are calculated and placed in the residt list." $\endgroup$ – Matthew Gunn Mar 8 '18 at 17:26
  • $\begingroup$ @Matthew Gunn That makes sense. So they are the residuals that go along with performing a linear transformation first then simply running a linear regression of the transformed data? $\endgroup$ – WaveX Mar 8 '18 at 17:30

Searching Google for the TI-89 manual I find,

Values for $a$, $b$, $r^2$ , and $r$ are displayed in the PowerReg output dialog box. The power regression equation is stored in Y1. Residuals for the power regression are calculated and placed in the resid list. The previous contents of resid are overwritten by the new data. Residuals associated with the linear fit of the transformed data are calculated and placed in the residt list.

Reading between the lines, my interpretation/guess is that residt would be residuals from the ordinary least squares regression:

$$\log y_i = \log a + b \log x_i + \epsilon_i$$

I'm not 100% sure though. You could easily check if that's indeed correct.

  • $\begingroup$ Doing a simple test with random points confirmed this! Thank you $\endgroup$ – WaveX Mar 8 '18 at 17:41

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