Exercise 2: Why Logistic Regression Is Still "Regression" — Possible Solution
====================================================================

WHAT STAYS THE SAME, PER THIS CHAPTER
------------------------------
Per this chapter, "logistic regression keeps ml1-3's own linear
combination of weighted features underneath — this is genuinely still
'regression' in that sense, which is exactly why the confusing name
persists." The core computation — multiplying each feature by a
learned weight and summing them, exactly ml1-3's own w1×feature1 +
w2×feature2 + b structure — is completely unchanged between the two
techniques. Both fit the same kind of linear combination of features.

WHAT CHANGES, PER THIS CHAPTER
------------------------------
Per this chapter, logistic regression "passes the result through the
sigmoid function before treating it as an answer" — an additional final
step layered on top of the same linear computation, squashing whatever
real number the linear combination produces into the (0, 1) range so
it can be read as a probability. This is the only structural difference
between the two techniques as this chapter describes them.

WHY THIS JUSTIFIES KEEPING THE WORD "REGRESSION"
------------------------------
"Regression" refers to the underlying technique of fitting a linear
combination of weighted features to data — exactly what both ml1-3's
plain linear regression and this chapter's logistic regression do at
their core. The sigmoid step doesn't replace that linear fitting
process; it's applied AFTER it, transforming the linear combination's
own raw output into a probability rather than changing how that raw
output itself gets computed and fit. Since the defining "regression"
step (fitting linear weights) is identical in both techniques, the name
accurately describes what's actually happening underneath, even though
the final, sigmoid-transformed output is used to make a category
prediction rather than a continuous one.

WHY THE NAME STILL CONFUSES MANY LEARNERS
------------------------------
The word "regression" is far more commonly associated with the KIND OF
OUTPUT a technique produces (continuous numbers, per ml1-3) than with
the specific fitting mechanism used internally — so a technique whose
final output is a category (Yes/No) intuitively sounds like it should
be called something else, "classification," which is in fact the name
of the broader task category logistic regression is actually used for.
The name reflects the internal mechanism, not the final task, which is
precisely the source of the confusion this chapter's own explanation
resolves.

WHY THIS WORKS AS AN ANSWER
------------------------------
It identifies precisely what's identical between the two techniques
(the linear weighted-feature-combination step) and precisely what's
different (the added sigmoid transformation), and explains why the name
"regression" tracks the shared internal mechanism rather than the
different final output type — which is exactly why the name persists
despite being used for a classification task.