An Ardent Fan of Television Game Shows Has Observed That

question 98

Essay

An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education. The results are as follows. $\begin{array}{|c|c|c|r|r|}\hline \text { Contestant } & \begin{array}{c}\text { Years of } \\\text { education }\end{array} & \text { Winnings } & \begin{array}{c}\text { Predicted } \\\text { values }\end{array} & \text { Residuals } \\\hline 1 & 11 & 750 & 754.2 & -4.167 \\\hline 2 & 15 & 400 & 397.5 & 2.500 \\\hline 3 & 12 & 600 & 665.0 & -65.000 \\\hline 4 & 16 & 350 & 308.3 & 41.667 \\\hline 5 & 11 & 800 & 754.2 & 45.833 \\\hline 6 & 16 & 300 & 308.3 & -8.333 \\\hline 7 & 13 & 650 & 575.8 & 74.167 \\\hline 8 & 14 & 400 & 486.7 & -86.667 \\\hline\end{array}$ Plot the residuals against the predicted values. Does the variance appear to be constant?

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Definitions:

Collectivistic Society

A society that prioritizes the group over the individual, emphasizing community, cooperation, and shared values.

Attributional Style

A person's habitual way of explaining the events of their life, particularly the causes of positive and negative events.

Individualistic Societies

Cultures where personal achievements and independence are valued over group goals and harmony, leading to a focus on individual rights and autonomy.