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

Problems

1. Given a set of ordered pairs (x, y) so that s_x = 1.6, s_y = 0.75, r = 0.55. What is the slope of the least-square regression line for these data?
   1. 1.82
   2. 1.17
   3. 2.18
   4. 0.26
   5. 0.78
2. 

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?

1. 1.71
2. –1.71
3. 2.29
4. 5.15
5. –2.29
3. 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?
   1. About one-third of the variation in hours spent exercising can be explained by hours spent watching television.
   2. A person who watches less television will exercise more.
   3. For each hour spent watching television, the predicted decrease in hours spent exercising is 0.58 hrs.
   4. There is a cause-and-effect relationship between hours spent watching television and a decline in hours spent exercising.
   5. 58% of the hours spent exercising can be explained by the number of hours watching television.
4. 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?
   1. –1.09
   2. –0.34
   3. 0.34
   4. 0.082
   5. 1.09
5. Consider the following residual plot:



Which of the following statements is (are) true?

1. The residual plot indicates that a line is a reasonable model for the data.
2. The residual plot indicates that there is no relationship between the data.
3. The correlation between the variables is probably non-zero.
1. I only
2. II only
3. I and III only
4. II and III only
5. I and II only
6. 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?
   1. A person who is 61 inches tall will weigh 104.6 pounds.
   2. For each additional inch of Height, Weight will increase on average by 3.6 pounds.
   3. There is a strong positive linear relationship between Height and Weight.
   1. I only
   2. II only
   3. III only
   4. II and III only
   5. I and II only
7. 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?
   1. 26.2
   2. 43.9
   3. –37.1
   4. –26.2
   5. 37.1
8. 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
   1. – 0.26
   2. 0.26
   3. 0
   4. 0.52
   5. – 0.52
9. 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:



What percent of the variation in SAT scores is explained by the regression of SAT score on GPA?

1. 62.1%
2. 72.3%
3. 88.8%
4. 94.2%
5. 78.8%