PYTHON · NUMPY

Which number can be a name

Show that a coefficient can only serve as an identity if it is individually identifiable, and find which one is.

01Challenge

The power model has four coefficients per joint. Decide which of them could carry an identity, and prove the others cannot.

Predict firstA model has four fitted coefficients. How many can serve as a hardware identity?

02Model

A fingerprint has to be a property of the hardware, not a choice the fitting procedure made. If two different coefficient values explain the measurements equally well, then whichever one you got is an accident of the optimiser, and it will be a different accident tomorrow. So before asking whether units differ, ask whether the number is pinned down at all. Run the standard errors and the answer is stark: one coefficient out of four is determined tightly enough to matter, and it is the copper term — the same term the datasheet tolerances pointed at. The physics and the statistics agree without being asked to.

03Guided practice

Build the regressor for a single joint, vary the richness of the trajectory set, and watch the conditioning and the per-parameter errors move together.

04Feedback

PASS WHEN You found the one coefficient that is a property of the hardware rather than of the fit.

If your run fails, check:

Only b, the copper-loss term, resolves tightly enough — 0.2 to 1.0% against a 21.5% signal.
The mechanical and viscous terms sit at 36 to 54% error even with rich excitation. A fingerprint using them would be mostly noise.
Excitation matters enormously: going from one travel distance to three moved the conditioning by ten orders of magnitude. Identifiability is a property of your experiment, not just of your model.

05Retrieve & space

Why can a non-identifiable parameter not serve as an identity?
Which coefficient carries the identity, and why is that physically unsurprising?
What happened to conditioning when the trajectory set gained two more travel distances?

06Mastery & project

Report identifiability per parameter before claiming any parameter means something.

Take a fitted model from your own work. For one parameter, estimate its standard error. Decide whether the value you have been quoting is pinned down or merely reported.

GO FURTHER · THE LIVE PLAYGROUND

Open the instrument ↗ · The coefficient this lesson selects is the one the instrument plots.

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PYTHON · NUMPY

Which number can be a name

Standard errors are given for four excitation designs. Decide which coefficients can serve as an identity.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you