Two-Variable Data Analysis Multiple Choice Practice Problems for AP Statistics (page 2)

By — McGraw-Hill Professional
Updated on Feb 5, 2011


  1. The correct answer is (d).
  2. Two-Variable Data Analysis Solutions to Practice Problems

  3. The correct answer is (e). The value of a residual = actual value – predicted value = 25 – [2.35 + 0.86(29)] = –2.29.
  4. The correct answer is (a). r2 = (–0.58)2 = 0.3364. This is the coefficient of determination, which is the proportion of the variation in the response variable that is explained by the regression on the independent variable. Thus, about one-third (33.3%) of the variation in hours spent exercising can be explained by hours spent watching television. (b) is incorrect since correlation does not imply causation. (c) would be correct if b = –0.58, but there is no obvious way to predict the response value from the explanatory value just by knowing r. (d) is incorrect for the same reason (b) is incorrect. (e) is incorrect since r, not r2, is given. In this case r2 = 0.3364, which makes (a) correct.
  5. The correct answer is (c). ln( y) = 1.64 – 0.88(3.1) = –1.088 Two-Variable Data Analysis Solutions to Practice Problems y = e–1.088 = 0.337.
  6. The correct answer is (c). The pattern is more or less random about 0, which indicates that a line would be a good model for the data. If the data are linearly related, we would expect them to have a non-zero correlation.
  7. The correct answer is (b). I is incorrect—the predicted weight of a person 61 inches tall is 104.6 pounds. II is a correct interpretation of the slope of the regression line (you could also say that "For each additional inch of Height, Weight is predicted to increase by 3.6 pounds). III is incorrect. It may well be true, but we have no way of knowing that from the information given.
  8. The correct answer is (c). The predicted score for the student is 273.5 + (91.2)(3) = 547.1. The residual is the actual score minus the predicted score, which equals 510 – 547.1 = –37.1.
  9. The correct answer is (b). Consider the expression for r. Two-Variable Data Analysis Solutions to Practice Problems. Adding 12 to each Y-value would not change sy. Although the average would be 12 larger, the differences y would stay the same since each Y-value is also 12 larger. By taking the negative of each X-value, each term Two-Variable Data Analysis Solutions to Practice Problems would reverse sign (the mean also reverses sign) but the absolute value of each term would be the same. The net effect is to leave unchanged the absolute value of r but to reverse the sign.
  10. The correct answer is (e). The question is asking for the coefficient of determination, r2 (R-sq on many computer printouts). In this case, r = 0.8877 and r2 = 0.7881, or 78.8%. This can be found on your calculator by entering the GPA scores in L1, the SAT scores in L2, and doing STAT CALC 1-Var Stats L1,L2.
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