AP Statistics – Chapter 3 Review
Multiple Choice Practice
1. Data on ages (in years) and prices (in $100) for ten cars of a specific model result in the regression line: . Given that 64% of the variation in price is explainable by variation in age, what is the value of the correlation coefficient r?
(a)
(b)
(c)
(d)
(e) There is insufficient information to answer this question.
2. Data are obtained from a random sample of women with regard to their ages and their monthly expenditures on health products. The resulting regression equation is: with r = .27. What percentage of the variation in expenditures can be explained by looking at ages?
(a) 0.23% (b) 23% (c) 7.29% (d) 27% (e) 52.0%
3. Which of the following statements about residuals are true?
I. The mean of the residuals is always zero.
II. The regression line for a residual plot is a horizontal line.
III. The standard deviation of the residuals gives a the typical prediction error of the regression line.
(a) I and II
(b) I and III
(c) II and III
(d) II and III
(e) None of the above gives the complete set of true responses.
4. If every man married a woman who was exactly 3 years younger than he, what would be the correlation between the ages of married men and women?
(a) Somewhat negative
(b) 0
(c) Somewhat positive
(d) Nearly 1
(e) 1
5. Suppose the correlation between two variables is r = .28. What will the new correlation be if .17 is added to all values of the x-variables, every value of the y-variable is doubled, and the two variables are interchanged?
(a) .28 (b) .45 (c) .56 (d) .90 (e) -.28
6. A simple random sample of 25 world-ranked tennis players provides the following statistics: Number of hours of practice per day: , . Yearly winnings: , . Correlation r = .23. Based on this data, what is the resulting linear regression equation?
(a)
(b)
(c)
(d)
(e)
7. There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model , where x is the number of chirps per minute and is the estimated temperature in degrees Fahrenheit. What is the predicted temperature for a cricket who chirps15 chirps per minute?
(a) 3.3°F (b) 74.7°F (c) 25.2°F (d) 49.5°F (e) 41.7°F
8. Using the LSRL from #7, find and interpret the residual in context for the striped ground cricket who chirped 18 chirps per minute while it was 80°F.
(a) Residual =4.6°F. The temperature was 4.6°F higher than what was expected for a striped ground cricket who chirped 18 chirps per minute.
(b) Residual = - 4.6 chirps. The striped ground cricket chirped 4.6 chirps less than what we expected at the temperature of 80°F.
(c) Residual =4.6 chirps. The striped ground cricket chirped 4.6 chirps more than what we expected at the temperature of 80°F.
(d) Residual = - 4.6°F. The temperature was 4.6°F lower than what was expected for a striped ground cricket who chirped 18 chirps per minute.
(e) Residual = 20.6°F. The temperature was 20.6°F higher than what we expected for a striped ground cricket who chirped 18 chirps per minute.
Multiple Choice Answers: 1. B, 2. C, 3. D, 4. E, 5. A, 6. A, 7. B, 8. D
Free Response Practice.
9. It is usual in finance to describe the returns from investing in a single stock by regressing the stock’s returns on the returns from the stock market as a whole. This helps us see how closely the stock follows the market. WE analyzed the monthly percent total return y on Philip Morris common stock and the monthly return x on the Standard & Poor’s 500 Index, which represents the market, for the period between July 1990 and May 1997. Here are the results:
A scatterplot shows no influential observations.
(a) Find the equation () of the least-squares line from this information. What percent of the variation (r2) in Philip Morris stock is explained by the linear relationship with the market as a whole? (Use: slope: , and intercept: )
(b) Explain carefully what the slope of the line tells us about how Phillip Morris stock responds to changes in the market.
(c) Calculate and interpret r2 in context.
10. Good runners take more steps per second as they speed up. Here are the average numbers of steps per second for a group of top female runners at different speeds. The speeds are in feet per second.
Speed (ft/s): / 15.86 / 16.88 / 17.50 / 18.62 / 19.97 / 21.06 / 22.11Steps per second: / 3.05 / 3.12 / 3.17 / 3.25 / 3.36 / 3.46 / 3.55
(a) You want to predict steps per second from running speed. Make a scatterplot of the data with this goal in mind.
(b) Describe the pattern of the data in context and find the correlation.
(c) Find the least-squares regression line of steps per second on running speed. Draw this line on your scatterplot.
(d) Does running speed explain most of the variation in the number of steps a runner takes per second? Calculate r2 and use it to answer this question.
(e) Predict the steps per second for a runner who has a speed of 17.65 ft/s.
(f) If you wanted to predict running speed from a runner’s steps per second, would you use the same line? Explain your answer. Would r2 stay the same?
11. Consider the following data from a small bookstore.
Number of Sales People Working / Sales (in $1000)2 / 10
3 / 11
7 / 13
9 / 14
10 / 18
10 / 20
12 / 20
15 / 22
16 / 22
20 / 26
(a) Make a scatterplot of Sales against Number of sales people working.
(b) Describe the scatterplot in context.
(c) Find the Least-Squares Regression line and correlation.
(d) Interpret the slope and y-intercept of the Least-Squares Regression line in context.
(f) Calculate and interpret the residual for the day that 12 people were working and they had $20,000 in sales.
(g) Using your calculator, sketch the residual plot. (h) The following regression analysis of the data was
Is the LSRL an appropriate model for the data? Why? found. Interpret s and r2 in context.