Game Winnings & Education
an Ardent Fan of Television Game

question 29

Essay

Game Winnings & Education
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 favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows.
$$\begin{array} { | c | c | c | } \hline \text { Contestant } & \text { Years of Education } & \text { Winnings } \\\hline 1 & 11 & 750 \\2 & 15 & 400 \\3 & 12 & 600 \\4 & 16 & 350 \\5 & 11 & 800 \\0 & 16 & 300 \\7 & 13 & 650 \\8 & 14 & 400 \\\hline\end{array}$$
-{Game Winnings & Education Narrative} Plot the residuals against the predicted values $\hat { y }$ .What does the graph tell you?

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Definitions:

Linear Trend Extrapolation

A forecasting method that uses historical data to predict future outcomes by fitting the data into a linear equation and projecting it forward.

Trend Extrapolation

The analytical process of using historical data to make predictions or forecasts about future trends.

Semantic Differential Scale

A survey or questionnaire tool that measures the meaning or connotations of a concept by using a series of bipolar adjectives.

Likert Scale

A psychometric scale commonly involved in research that employs questionnaires, often used to measure attitudes or opinions with a degree of agreement or disagreement.