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The Manager of a Fast Food Restaurant Wants to Determine

Question 133

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The manager of a fast food restaurant wants to determine how sales in a given week are related to the number of discount vouchers (#) printed in the local newspaper during the week. The number of vouchers and sales ($000s) from 10 randomly selected weeks is given below with Excel regression output.  Number of vouchers  Sales 412.8715.4513.9311.21918.71017.9816.8615.9311.5513.9\begin{array} { | c | c | } \hline \text { Number of vouchers } & \text { Sales } \\\hline 4 & 12.8 \\\hline 7 & 15.4 \\\hline 5 & 13.9 \\\hline 3 & 11.2 \\\hline 19 & 18.7 \\\hline 10 & 17.9 \\\hline 8 & 16.8 \\\hline 6 & 15.9 \\\hline 3 & 11.5 \\\hline 5 & 13.9 \\\hline\end{array}  SUMMARY OUTPUT  Regression Statistics  Multiple R 0.8524 R Square 0.7267 Adjuted R Square 0.6925 Standard Error 1.4301 Observations 10.0000 ANOVA  Sgnificance dfSSMSFF Regression 1.000043.498243.498221.26820.0017 Residual 8.000016.36182.0452 Total 9.000059.8600 Coefficients  Standard  Error  t Stat  P-value  Lower 95%  Upper 95% Interoept 11.56760.834113.86790.00009.644113.4912 Number of voudhers 0.46180.10014.61170.00170.23090.6927\begin{array}{|l|c|c|c|c|c|c|}\hline \text { SUMMARY OUTPUT }\\\hline \text { Regression Statistics } & \\\hline \text { Multiple R } & 0.8524 \\\hline \text { R Square } & 0.7267 \\\hline \text { Adjuted R Square } & 0.6925 \\\hline \text { Standard Error } & 1.4301 \\\hline \text { Observations } & 10.0000 \\\hline\\\hline\text { ANOVA }\\\hline & & & & & \text { Sgnificance } \\& d f & S S & M S & F & F \\\hline \text { Regression } & 1.0000 & 43.4982 & 43.4982 & 21.2682 & 0.0017 \\\hline \text { Residual } & 8.0000 & 16.3618 & 2.0452 & & \\\hline \text { Total } & 9.0000 & 59.8600 & & & \\\hline\\\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \begin{array}{c}\text { Upper } \\95 \%\end{array} \\\hline \text { Interoept } & 11.5676 & 0.8341 & 13.8679 & 0.0000 & 9.6441 & 13.4912 \\\hline \text { Number of voudhers } & 0.4618 & 0.1001 & 4.6117 & 0.0017 & 0.2309 & 0.6927 \\\hline\end{array} Interpret the coefficient of determination.

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72.67% of the variation in wee...

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