Exercise 1: Why Plain Linear Regression Genuinely Breaks on a Yes/No Target — Possible Solution
====================================================================

WHAT THE CHAPTER SPECIFICALLY CLAIMS
------------------------------
Per this chapter, "fitting ml1-3's own plain linear regression directly
against a 0/1-coded target would produce genuine nonsense: nothing stops
the fitted line from predicting -0.3 or 1.4 for some employees —
numbers with no sensible reading as 'how likely is this person to
leave.'"

WHY LINEAR REGRESSION CAN PRODUCE THESE VALUES AT ALL
------------------------------
Per ml1-3, linear regression fits an unbounded straight line (or
hyperplane): price = w1×mileage + w2×year + b, with no built-in limit
on how large or small the output can be — the fitted line is free to
extend infinitely in either direction as the input features vary. When
the target is 0/1-coded left_company instead of price, the exact same
unbounded linear formula still applies — nothing about the fitting
process itself knows the target is only ever supposed to be 0 or 1, so
it produces whatever real number the linear combination of weighted
features happens to compute, with no mechanism preventing that number
from landing outside the 0-1 range for some combination of input
values.

WHY THIS IS A CONCRETE PROBLEM, NOT AN ABSTRACT MISMATCH
------------------------------
A prediction of -0.3 or 1.4 isn't merely "a slightly odd-looking
number" — it has no coherent interpretation at all as a probability or
as any meaningful prediction about whether someone will leave.
Probabilities are only meaningful between 0 (definitely won't happen)
and 1 (definitely will happen); a value like -0.3 doesn't correspond to
"less than definitely won't happen" in any real sense — it's simply
outside the space of values the question "how likely is this person to
leave" can even be answered in. This is a genuine, demonstrable
failure of the output to mean anything, not a stylistic or conventional
mismatch that could be waved away.

WHY THIS ISN'T JUST "THE WRONG TOOL IN THE ABSTRACT"
------------------------------
Calling it "the wrong tool" without this explanation would leave a
reader without any real reason to believe it — this chapter instead
shows a specific, concrete failure mode (predictions escaping the only
range in which the target actually makes sense) that follows
mechanically and inevitably from linear regression's own unbounded
output, rather than asserting a rule to be taken on faith.

WHY THIS WORKS AS AN ANSWER
------------------------------
It explains precisely why linear regression's own output is unbounded
(per ml1-3's own formula), and explains why a value outside 0-1 isn't
just unusual-looking but genuinely uninterpretable as an answer to the
actual question being asked, which is exactly the concrete failure this
chapter points to rather than a vague tool mismatch.