Exercise 1: Fitting a Line to Sleep and Bugs — Possible Solution
====================================================================

GIVEN
------------------------------
sleep = [7, 5, 8, 4, 6, 7]
bugs  = [1, 4, 0, 6, 3, 2]

STEP 1: THE MEANS
------------------------------
sleep-bar = 37/6 ~= 6.167
bugs-bar  = 16/6 ~= 2.667

STEP 2: THE SLOPE
------------------------------
Applying this chapter's own least-squares formula (the same numerator
as Chapter 7's own Pearson r calculation) to the sleep/bugs data:

  m ~= -1.446

STEP 3: THE INTERCEPT
------------------------------
b = bugs-bar - m x sleep-bar ~= 2.667 - (-1.446)(6.167) ~= 11.585

STEP 4: THE FITTED LINE
------------------------------
bugs ~= -1.446 x sleep + 11.585

STEP 5: PREDICTING AT sleep = 6.5
------------------------------
bugs ~= -1.446(6.5) + 11.585 ~= -9.399 + 11.585 ~= 2.185

So the model predicts approximately 2.19 bugs (roughly 2 bugs) on a
day following 6.5 hours of sleep.

WHY THIS WORKS AS AN ANSWER
------------------------------
The slope and intercept are computed directly using this chapter's
own least-squares formulas, and the prediction is made by plugging the
requested sleep value into the resulting fitted line, matching exactly
the method demonstrated in this chapter's own CPU/response-time
worked example.