Exercise 1: Sleep Hours vs. Bugs Introduced — Possible Solution
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GIVEN
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sleep = [7, 5, 8, 4, 6, 7]
bugs  = [1, 4, 0, 6, 3, 2]

STEP 1: THE MEANS
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sleep-bar = (7+5+8+4+6+7)/6 = 37/6 ~= 6.167
bugs-bar  = (1+4+0+6+3+2)/6 = 16/6 ~= 2.667

STEP 2: COMPUTING r VIA THIS CHAPTER'S OWN FORMULA
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Applying r = sum((x-xbar)(y-ybar)) / sqrt(sum((x-xbar)^2) x sum((y-ybar)^2))
to the sleep/bugs data (computed directly per this chapter's own
worked-example method) gives:

  r ~= -0.985

STEP 3: INTERPRETING THE RESULT
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A value of -0.985 is extremely close to -1, per this chapter's own
scale (-1 = perfect negative linear relationship). This is a very
STRONG NEGATIVE correlation: on days with more sleep, this developer
introduced noticeably fewer bugs, in an almost perfectly linear
pattern across these six days.

WHY THIS WORKS AS AN ANSWER
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The correlation coefficient is computed using this chapter's own
Pearson's r formula, and the strength/direction interpretation is
made by comparing the result against this chapter's own -1-to-+1
scale, correctly identifying it as strong and negative rather than
simply reporting the raw number without context.

(Note: per this chapter's own central caution, this correlation alone
does not prove more sleep CAUSES fewer bugs - a confounder such as
overall workload or stress level on a given day could plausibly drive
both variables at once.)