At this time, this isn't an answer as such, but rounds out more of what the original poster should have included.
Plus, this reply points out that the issue doesn't seem to really interfere with observing what the plot is meant to illustrate.
Replicating the issue and getting the full error traceback that should have been included in the post
Searching 'Replicate Andrew's example on PCA' in Google, lead me to the notebook here, which looks to be the same as the OP is running.
I then obtained that notebook and uploaded it to a fresh remote session (served by the MyBinder service) started from the launch badge here. (Or you can just click here to get yourself a session such as I describe, plus save yourself the steps of switching to JupyterLab for ease in upload of the notebook.)
(But actually use the notebook I modified here because it gets the linked script file needed and sets up the environment with a couple things the session didn't already have.).
After the session comes up, if you are in the Jupyter Notebook mode your URL will look something like https://hub.binder.curvenote.dev/user/fomightez-clust-analysis-binder-w8zoszhl/notebooks/index.ipynb. Delete the notebooks/index.ipynb from the end of the URL in your address bar and replace it with lab to give the address bar something like https://hub.binder.curvenote.dev/user/fomightez-clust-analysis-binder-w8zoszhl/lab and hit enter. Okay the leave step and you should have the page reload as JupyterLab and you can easily drag and drop the notebook from your local machine to the running session by clicking on it on your local machine and dragging it into the file browser panel on the left side of the JupyterLab view and releasing the moust. Use my version of th enotebook from the gist though, available here, as I added stuff at the top needed to make it run in the MyBinder served session with the environment I had set up for looking into clusters.
The error seen after running plot_widget() cell under the section 'Visualizing the PCA algorithm' (look for In [19] in front of the cell in the rendering here) is:
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
File /srv/conda/envs/notebook/lib/python3.10/site-packages/ipywidgets/widgets/interaction.py:243, in interactive.update(self, *args)
241 value = widget.get_interact_value()
242 self.kwargs[widget._kwarg] = value
--> 243 self.result = self.f(**self.kwargs)
244 show_inline_matplotlib_plots()
245 if self.auto_display and self.result is not None:
File ~/pca_utils.py:285, in plot_widget.<locals>.update(angle)
283 def update(angle):
284 ang = angle
--> 285 with fig.batch_update():
286 p0r = rotation_matrix(ang)@p0
287 p1r = rotation_matrix(ang)@p1
NameError: free variable 'fig' referenced before assignment in enclosing scopeSurprisingly, that error cannot be viewed here in context because it seems to put the error somehow in the widget and nbviewer doesn't show that text. (Nor does GitHub here, although that is not as surprising as the GitHub rendering is more limited than nbviewer in many ways.)
Although this is usually frowned upon, I will add a screenshot to show it context as this is an unusual case:
However, I don't actually see the error being much of a problem. The plot is still interactive because as I slide the 'angle' slider, it updates and changes multiple aspects of the two plots. Hence, it still seems to illustrate what the notebook author wanted. And so I'm not really seeing this be a big problem?
From the error it looks like pca_utils.py invokes a reference to fig using the line with fig.batch_update():, and that maybe it is doing that too early or not in the right way given modern ipywidgets. However, I believe the course organizers would need to deal with it as that file pca_utils.py comes from them and not ipywidgets or the notebook. Despite that, like I said it doesn't seem to interfere with the plot showing what it is meant to show at this time.