An Ardent Fan of Television Game Shows Has Observed That

question 67

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 and performs a simple linear regression, with the Excel output provided. $$\begin{array} { | c | c | c | } \hline \text { Contestant } & \begin{array} { c } \text { Years of } \\\text { education }\end{array} & \text { Winnings } \\\hline 1 & 11 & 750 \\\hline 2 & 15 & 400 \\\hline 3 & 12 & 600 \\\hline 4 & 16 & 350 \\\hline 5 & 11 & 800 \\\hline 6 & 16 & 300 \\\hline 7 & 13 & 650 \\\hline 8 & 14 & 400 \\\hline\end{array}$$ $\begin{array}{|l|r|c|c|c|c|c|}\hline \begin{array}{l}\text { SUMMARY } \\\text { OUTPUT }\end{array} & & \\\hline \begin{array}{c}\text { Regression } \\\text { Statistios }\end{array} & & \\\hline \text { Multiple R } & 0.9583798 & \\\hline \text { R Square } & 0.9184918 & \\\hline \text { Adjusted R Square } & 0.9049071 & \\\hline \text { Standard Error } & 59.395099 & \\\hline \text { Obseruations } & 8 & \\\hline & & \\\hline \text { ANOVA } & & & & & & \\\hline & \text { df } & S S & M S & F & \begin{array}{c}\text { Significance } \\F\end{array} & \\\hline \text { Regression } & 1 & 238520.8333 & 238520.8 & 67.6122047 & 0.00017466 & \\\hline \text { Residual } & 6 & 21166.66667 & 3527.778 & & & \\\hline \text { Total } & 7 & 259687.5 & & & & \\\hline & & \\\hline & \text { coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { tstat } & \text { Pvalue } & \text { Lower 95\% } & \begin{array}{c}\text { Upper } \\95 \%\end{array} \\\hline \text { Intercept } & 1735 & 147.8926037 & 11.73149 & 2.3148 E-05 & 1373.11984 & 2096.8802 \\\hline \text { Years of education } & -89.16667 & 10.84401183 & 8.222664 & 0.00017466 & -115.70101 & -62.63233 \\\hline\end{array}$ a. Determine the least squares regression line.
b. Interpret the value of the slope of the regression line.
c. Determine the standard error of estimate, and describe what this statistic tells you about the regression line.
d. Interpret the coefficient of correlation

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Definitions:

Audi/o

A prefix meaning related to hearing or sound.

Organ of Corti

A structure located in the cochlea of the inner ear, responsible for converting sound vibrations into nerve impulses.

Otorhinolaryngology

A surgical subspecialty within medicine that deals with conditions of the ear, nose, and throat (ENT) and related structures of the head and neck.

Fenestration

A surgical procedure that creates a new opening, especially used in reference to procedures involving the ear to improve hearing.