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

question 1

Essay

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. Researchers believe that this may be the result of perceived differences in personality. 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 (average
girls' rating, average boys' rating) for a given trait.

Linear Fit
MRating $= - 0.765 + 0.714$ FRating
Summary of Fit

$\begin{array}{ll}\text { RSquare } & 0.552 \\\text { RSquare Adj } & 0.529 \\\mathrm{~s} & 0.490\end{array}$

$\begin{array}{l}\text { Analysis of Variance }\\\begin{array}{lrrcr}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F Ratio } \\\text { Model } & 1 & 5.63 & 5.63 & 23.45 \\\text { Error } & 19 & 4.56 & 0.24 & \text { Prob }>\text { F } \\\text { C. Total } & 20 & 10.20 & & 0.0001\end{array}\end{array}$
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 was given an
average of 0.0 ("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 on average 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?

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Definitions:

Net Operating Income

The profit realized from a business's operations after subtracting all operation-related expenses from gross income.

Contribution Margin

The difference between sales revenue and variable costs, indicating how much revenue is contributing to the fixed costs and net profit after covering the variable costs.

Gross Margin

The difference between revenue and cost of goods sold divided by revenue, expressed as a percentage, indicating the percentage of sales revenue that turns into profit.

Shareholder Wealth

The overall value that shareholders gain from their investment in a company, often measured by stock price appreciation and dividends received.