Exercise 2: R-squared for the Sleep/Bugs Model — Possible Solution ==================================================================== GIVEN ------------------------------ r ~= -0.985 (from Chapter 7's own sleep/bugs correlation calculation) STEP 1: APPLYING R-SQUARED = r^2 ------------------------------ Per this chapter's own R^2 = r^2 relationship: R^2 = (-0.985)^2 ~= 0.971 STEP 2: INTERPRETING THE RESULT IN PLAIN TERMS ------------------------------ An R^2 of approximately 0.971 means about 97.1% of the day-to-day variation in the number of bugs introduced is explained by hours of sleep alone, in this simple linear model. Only about 2.9% of the variation is left unaccounted for by the fitted line - a very strong fit, similar in strength to this chapter's own CPU/response-time example (R^2 ~= 0.994). WHY THIS WORKS AS AN ANSWER ------------------------------ R-squared is computed directly by applying this chapter's own R^2=r^2 shortcut to the already-known r value from Chapter 7, avoiding a separate recalculation, and the plain-language interpretation states specifically what percentage of variance is explained versus left unexplained rather than just reporting the raw number.