Exercise 3: Why CPU=5% Is Just as Risky an Extrapolation as CPU=100% — Possible Solution ==================================================================================== THE KEY MISCONCEPTION TO ADDRESS ------------------------------ It's tempting to think a "small," seemingly modest number like 5% CPU usage must be safer to predict than an extreme number like 100% - but per this chapter's own extrapolation warning, what actually matters is not how large or small the number itself looks, but whether it falls WITHIN the range of x-values the line was actually fitted from. WHY 5% IS OUTSIDE THE OBSERVED RANGE, JUST LIKE 100% IS ------------------------------ This chapter's own worked example was built entirely from CPU values between 40% and 70%. A value of 5% CPU usage is just as far outside that observed range on the low end as 100% is on the high end - neither value has any actual data nearby to confirm the line still behaves linearly there. The model has no evidence at all about how response time behaves once CPU usage drops well below the observed minimum, exactly the same blind spot it has above the observed maximum. WHAT COULD GO WRONG SPECIFICALLY AT THE LOW END ------------------------------ Just as very high CPU usage might cause a sharper-than-linear degradation the fitted line can't predict, very low CPU usage might have its own different behavior the data never captured - for example, a fixed baseline response time (network latency, a minimum processing floor) that the response time can never drop below no matter how idle the CPU gets. The straight line, if extrapolated downward, would incorrectly keep predicting an ever-decreasing response time with no floor, when reality likely levels off instead. WHY THIS WORKS AS AN ANSWER ------------------------------ The explanation directly challenges the assumption that "small number = safe prediction," grounding the answer in this chapter's own stated rule that trustworthiness depends specifically on falling within the observed x-range, not on the numeric size of the value itself, and gives a concrete plausible reason the linear relationship could break down in the unobserved low-CPU region too.