As early as 3 years of age, children begin to show preferences for playing with members of their own sex, and report having more same-sex than opposite-sex friends. In a study of 3rd and 4th graders' views on 48 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 plot of the data is presented below. A single point represents the (average girls' rating, average boys' rating) for a given trait. Linear Fit
MRating = −0.765 + 0.714 FRating
a)Circle the single point which represents the most influential observation. What aspect of this point makes it the most influential?
b)Suppose a personality trait similar to those used in the survey were given a 0.0 rating ("can't tell") by the girls. The predicted boys' average rating would be closest to which of the 5 categories described above?
c)The traits plotted above are those the researchers believe are "positive" traits, such as "mature," "honest," and "polite." The researchers thought that girls would rate these positive traits as characteristic of girls to a greater extent than boys would. What aspects of the plot and/or regression analysis presented above are consistent with this thinking?

Question

As early as 3 years of age, children begin to show preferences for playing with members of their own sex, and report having more same-sex than opposite-sex friends. In a study of 3rd and 4th graders' views on 48 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 plot of the data is presented below. A single point represents the (average girls' rating, average boys' rating) for a given trait.  Linear Fit
MRating = −0.765 + 0.714 FRating  ​  ​
a)Circle the single point which represents the most influential observation. What aspect of this point makes it the most influential?
b)Suppose a personality trait similar to those used in the survey were given a 0.0 rating ("can't tell") by the girls. The predicted boys' average rating would be closest to which of the 5 categories described above?
c)The traits plotted above are those the researchers believe are "positive" traits, such as "mature," "honest," and "polite." The researchers thought that girls would rate these positive traits as characteristic of girls to a greater extent than boys would. What aspects of the plot and/or regression analysis presented above are consistent with this thinking?

Quizplus · Accepted Answer

The Answer of As early as 3 years of age, children begin to show preferences for playing with members of their own sex, and report having more same-sex than opposite-sex friends. In a study of 3rd and 4th graders' views on 48 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 plot of the data is presented below. A single point represents the (average girls' rating, average boys' rating) for a given trait.  Linear Fit
MRating = −0.765 + 0.714 FRating  ​  ​
a)Circle the single point which represents the most influential observation. What aspect of this point makes it the most influential?
b)Suppose a personality trait similar to those used in the survey were given a 0.0 rating ("can't tell") by the girls. The predicted boys' average rating would be closest to which of the 5 categories described above?
c)The traits plotted above are those the researchers believe are "positive" traits, such as "mature," "honest," and "polite." The researchers thought that girls would rate these positive traits as characteristic of girls to a greater extent than boys would. What aspects of the plot and/or regression analysis presented above are consistent with this thinking?

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