An Ardent Fan of Television Game Shows Has Observed That

question 63

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. $$\begin{array} { | c | c | c | } \hline \text { Contestant } & \begin{array} { c } \text { Years of } \\\text { education }\end{array} & \text { Winnings } \\\hline 1 & 11 & 750 \\\hline 2 & 15 & 400 \\\hline 3 & 12 & 600 \\\hline 4 & 16 & 350 \\\hline 5 & 11 & 800 \\\hline 6 & 16 & 300 \\\hline 7 & 13 & 650 \\\hline 8 & 14 & 400 \\\hline\end{array}$$ Determine the coefficient of determination and discuss what its value tells you about the two variables.

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Definitions:

Compounded Quarterly

Interest calculated on an investment or debt four times a year.

Population Decrease

A decline in the number of people living in a specific area, often due to factors like emigration, lower birth rates, or increased mortality rates.

Quarterly Compounded

A method where interest is calculated and added to the principal balance four times a year.

Nominal Interest Rate

The rate of interest before adjustment for inflation, representing the face value of borrowing or lending.