In a study of the interests of early adolescents, both boys and girls were asked to indicate their degree ofinterest in several topics by rating each on a seven-point scale (one meaning low interest, sevenmeaning high interest). The students were interviewed by the school counselor and their responseswere recorded. The students were in grades 5 through 9 with ages ranging from 10 to 15. The meanage was 12.6 for both the boys and the girls. The following table gives the average interest ratings forthe two groups on 25 topics.LoveLifeEarly Adolescent InterestsTopicMoneyPeopleOpposite SexMusicPeaceReligionSocial MediaTelevision.SportsMoviesCarsSchoolArtTeachersMagazinesSocial IssuesAnimalsMotorcyclesDeathWarAlcoholCigarettesDrugsGirls6.56.46.36.16.06.05.85.55.55.35.25.25.04.44.44.34.23.83.63.42.31.91.71.71.5Boys6.46.2ܩ ܩ ܩ ܩ6.55.66.25.35.55.15.25.56.15.45.73.33.13.64.13.63.55.7565PNNышш6792.02.71.91.61.6The scatterplot and regression line for these data are given on the next page, along with the questionsthat need to be answered. Interst Rating for Boys7.06.05.04.03.02.01.01.02.0Early Adolescent Interests3.04.0Interest Rating for Girls5.06.07.01. Describe the form, direction, and strength of the relationship between these variables.2.Graph the line y = x on the coordinate system above [hint: the graph of y = x goes through thepoints (1, 1), (2, 2), (3, 3), etc.]. Notice that the regression line lies very close to the line y = x.What does this tell you about the interest ratings of boys and girls on average?3. Identify the topic whose point is the largest vertical distance above the regression line. What doesthis mean in terms of the difference in interest ratings between boys and girls?4. Identify the topic whose point is the largest vertical distance below the regression line. What doesthis mean in terms of the difference in interest ratings between boys and girls?5. Notice the cluster of several points near the lower left corner of the scatterplot.a.What can you say about the interest ratings of boys and girls for these topics?b. Identify those topics.c. Do you think that early adolescents really are not interested in these topics?d. What might be another explanation for why these ratings came out so low?e. What other questions might this raise about the results?6. If you were to repeat this study for students in your school district, how would you plan the study sothat you could learn, as accurately as possible the true interest levels for all of the topics being askedabout?

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