Can you help me with problem 3.45?

140 CHAPTER 3 | Numerical Descriptive Measures In summary, the coefficient of correlation indicates the linear relationship, or association, between two numerical variables. When the coefficient of correlation gets closer to +1 or -1, the linear relationship between the two variables is stronger. When the coefficient of correlation is near 0, little or no linear relationship exists. The sign of the coefficient of correlation indicates whether the data are positively correlated (the larger values of X are typically paired with the larger values of Y) or negatively correlated (the larger values of X are typically paired with the smaller values of 1). The existence of a strong correlation does not imply a causation effect. It only indicates the tendencies present in the data. PROBLEMS FOR SECTION 3.5 LEARNING THE BASICS c. Which do you think is more valuable in expressing the relation- 3.44 The following is a set of data from a sample of n = 11 items: ship between calories and sugar-the covariance or the coeffi- cient of correlation? Explain. X 7 5 3 6 10 12 9 15 18 d. Based on (a) and (b), what conclusions can you reach about the Y 21 15 24 9 18 30 36 12 27 45 54 relationship between calories and sugar? a. Compute the covariance. 3.47 Movie companies need to predict the gross receipts of indi- b. Compute the coefficient of correlation. vidual movies once a movie has debuted. The data, shown below c. How strong is the relationship between X and )? Explain. and stored in Potter Movies , are the first weekend gross, the U.S gross, and the worldwide gross (in $millions) of the eight Harry APPLYING THE CONCEPTS Potter movies: 3.45 A study of 267 college students investigated the impact of smartphones on student connectedness and out-of-class involve- First U.S. Worldwide Weekend ment. One finding showed that students reporting a higher per- Title Gross Gross ceived usefulness of smartphones in educational settings used their Sorcerer's Stone 90.295 317.558 976.458 smartphone a higher number of times to send or read email for class Chamber of Secrets 88.357 261.988 878.988 purposes than students reporting a lower perceived usefulness of Prisoner of Azkaban 93.687 249.539 795.539 smartphones in educational settings. Goblet of Fire 102.335 290.013 896.013 Source: Liu X, et al, "The Impact of Smartphone Educational Use on Student Order of the Phoenix 77.108 292.005 938.469 Connectedness and Out-of-Class Involvement." The Electronic Journal of Half-Blood Prince 77.836 301.460 934.601 Communication (2016). Deathly Hallows Part 125.017 295.001 955.417 a. Does the study suggest that perceived usefulness of smartphones Deathly Hallows Part 2 169.189 381.011 1,328.111 in educational settings and use of smartphones for class purposes are positively correlated or negatively correlated? Source: Data extracted from www.the-numbers.com/interactive/comp- b. Do you think that there might be a cause-and-effect relationship Harry-Potter.php. between perceived usefulness of smartphones in educational settings and use of smartphones for class purposes? Explain. a. Calculate the covariance between first weekend gross and U.S. gross, first weekend gross and worldwide gross, and U.S. gross SELF 3.46 The file Cereals lists the calories and sugar, in TEST and worldwide gross. grams, in one serving of seven breakfast cereals: b. Calculate the coefficient of correlation between first weekend gross and U.S. gross, first weekend gross and worldwide gross, Cereal Calories Sugar and U.S. gross and worldwide gross. Kellogg's All Bran 80 6 c. Which do you think is more valuable in expressing the relation- Kellogg's Corn Flakes 100 ship between first weekend gross, U.S. gross, and worldwide Wheaties 100 gross-the covariance or the coefficient of correlation? Explain. Nature's Path Organic 110 d. Based on (a) and (b), what conclusions can you reach about Multigrain Flakes the relationship between first weekend gross, U.S. gross, and Kellogg's Rice Krispies 130 4 worldwide gross? Post Shredded Wheat 190 3.48 The file Mobile Speed contains the overall download and Vanilla Almond upload speeds in Mops for eight carriers in the U.S. Kellogg's Mini Wheats 200 10 Source: Data extracted from Tom's Guide, "Fastest Wireless Network 2019: It's Not Even Close," bitly/2PcGIQE. a. Calculate the covariance. a. Calculate the covariance between download speed and upload b. Calculate the coefficient of correlation. speed