Two-Variable Data Analysis Multiple Choice Practice Problems for AP Statistics (page 2)
Review the following concepts if necessary:
- Scatterplots for AP Statistics
- Correlation for AP Statistics
- Lines of Best Fit for AP Statistics
- Residuals for AP Statistics
- Coefficient of Determination for AP Statistics
- Outliers and Influential Observations for AP Statistics
- Transformations to Achieve Linearity for AP Statistics
- Given a set of ordered pairs (x, y) so that sx = 1.6, sy = 0.75, r = 0.55. What is the slope of the least-square regression line for these data?
- A study found a correlation of r = –0.58 between hours per week spent watching television and hours per week spent exercising. That is, the more hours spent watching television, the less hours spent exercising per week. Which of the following statements is most accurate?
- About one-third of the variation in hours spent exercising can be explained by hours spent watching television.
- A person who watches less television will exercise more.
- For each hour spent watching television, the predicted decrease in hours spent exercising is 0.58 hrs.
- There is a cause-and-effect relationship between hours spent watching television and a decline in hours spent exercising.
- 58% of the hours spent exercising can be explained by the number of hours watching television.
- A response variable appears to be exponentially related to the explanatory variable. The natural logarithm of each y-value is taken and the least-squares regression line is found to be ln(y) = 1.64 – 0.88x. Rounded to two decimal places, what is the predicted value of y when x = 3.1?
- Consider the following residual plot:
- The residual plot indicates that a line is a reasonable model for the data.
- The residual plot indicates that there is no relationship between the data.
- The correlation between the variables is probably non-zero.
- I only
- II only
- I and III only
- II and III only
- I and II only
- Suppose the LSRL for predicting Weight (in pounds) from Height (in inches) is given by Weight = –115 + 3.6 (Height). Which of the following statements is correct?
- A person who is 61 inches tall will weigh 104.6 pounds.
- For each additional inch of Height, Weight will increase on average by 3.6 pounds.
- There is a strong positive linear relationship between Height and Weight.
- I only
- II only
- III only
- II and III only
- I and II only
- A least-squares regression line for predicting performance on a college entrance exam based on high school grade point average (GPA) is determined to be Score = 273.5 + 91.2 (GPA). One student in the study had a high school GPA of 3.0 and an exam score of 510. What is the residual for this student?
- The correlation between two variables X and Y is –0.26. A new set of scores, X* and Y*, is constructed by letting X* = –X and Y* = Y +12. The correlation between X* and Y* is
- – 0.26
- – 0.52
- A study was done on the relationship between high school grade point average (GPA) and scores on the SAT. The following 8 scores were from a random sample of students taking the exam:
The regression line for the two-variable dataset given above is = 2.35 + 0.86x. What is the value of the residual for the point whose x-value is 29?
Which of the following statements is (are) true?
What percent of the variation in SAT scores is explained by the regression of SAT score on GPA?
- The correct answer is (d).
- The correct answer is (e). The value of a residual = actual value – predicted value = 25 – [2.35 + 0.86(29)] = –2.29.
- 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.
- The correct answer is (c). ln( y) = 1.64 – 0.88(3.1) = –1.088 y = e–1.088 = 0.337.
- 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.
- 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.
- 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.
- The correct answer is (b). Consider the expression for r. . 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 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.
- 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.
Add your own comment
Today on Education.com
WORKBOOKSMay Workbooks are Here!
ACTIVITIESGet Outside! 10 Playful Activities
Local SAT & ACT Classes
- Kindergarten Sight Words List
- The Five Warning Signs of Asperger's Syndrome
- What Makes a School Effective?
- Child Development Theories
- Why is Play Important? Social and Emotional Development, Physical Development, Creative Development
- 10 Fun Activities for Children with Autism
- Test Problems: Seven Reasons Why Standardized Tests Are Not Working
- Bullying in Schools
- A Teacher's Guide to Differentiating Instruction
- Should Your Child Be Held Back a Grade? Know Your Rights