The correlation coefficient for number of cans of beer and BAC is 0.89. Calculate R^2 and interpret it in context.

Question

BlackTom AI · Accepted Answer

The problem asks us to compute R^2 from a given correlation coefficient and interpret the result in context.
Option 1: 'R^2 = .79; Approximately 79% of the variability in blood alcohol content can be explained by number of cans of beer consumed.' Here, squaring r = 0.89 gives R^2 = 0.7921, which rounds to 0.79. The interpretation correctly states that about 79% of the variation in BAC is explained by the number of beer cans, leaving roughly 21% due to other factors. This option aligns with the math and the conceptual meaning of R^2.
Option 2: 'R^2 = .94; Approximately 94% of the variability in blood alcohol content can be explained by number of cans of beer consumed.' Squaring 0.89 does not yield 0.94; 0.89^2 is 0.7921, so this value is incorrect. The interpretation would also be inaccurate since the numeric result is wrong.
Option 3: 'R^2 = .79; Approximately 79% of the variability in blood alcohol content cannot be explained by number of cans of beer consumed.' This statement flips the interpretation. If R^2 is 0.79, it means 79% can be explained, not cannot be explained. The phrasing makes this choice incorrect despite the correct numeric value.
Option 4: 'R^2 = .94; Approximately 94% of the variability in blood alcohol content cannot be explained by number of cans of beer consumed.' This combines an incorrect R^2 with an incorrect interpretation (and also uses the negation of the explanatory power). Since both the statistic and the interpretation are wrong, this is clearly false.
In summary, the correct calculation is R^2 = 0.89^2 ≈ 0.79, and the proper interpretation is that about 79% of the variability in BAC is explained by the number of beer cans consumed, with residual variability attributed to other factors.

The correlation coefficient for number of cans of beer and BAC is 0.89. Calculate R^2 and interpret it in context.Single choice

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