An Ardent Fan of Television Game Shows Has Observed That

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