As Early as 3 Years of Age, Children Begin to Show

Essay

As early as 3 years of age, children begin to show preferences for playing withmembers of their own sex, and report having more same-sex than opposite-sexfriends. Researchers believe that this may be the result of perceived differences inpersonality. In a study of 3rd and 4th graders' views on a number personality traits,children were asked to rate on a "5-point" scale:-2 = "someone possessing that trait is probably a boy"-1 = "someone possessing that trait might be a boy"0 = "can't tell"1 = "someone possessing that trait might be a girl"2 = "someone possessing that trait is probably a girl"A scatterplot of the data is presented below. A single point represents the (averagegirls' rating, average boys' rating) for a given trait. a) Circle the single point which represents the most influential observation. Whataspect of this point makes it the most influential?
b) Suppose a personality trait similar to those used in the survey was given anaverage of 0.0 ("can't tell") by the girls. The predicted boys' average rating wouldbe closest to which of the 5 categories described above?
c) The traits plotted above are those the researchers believe are "positive" traits, suchas "mature," "honest," and "polite." The researchers thought that on average girlswould rate these positive traits as characteristic of girls to a greater extent thanboys would. What aspects of the plot and/or regression analysis presented aboveare consistent with this thinking?