The Manager of a Fast Food Restaurant Wants to Determine

question 136

Essay

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. $\begin{array}{|c|l|l|r|r|l|r|}\hline \begin{array}{c}\text { Number of } \\\text { vouchers }\end{array} & \text { Sales } &{\text { Number ofvouchers }} & &&{\text { Sales }} & \\\\\hline 4 & 12.8 & \text { Mean } & 7 &&\text { Mean } & 14.8 \\\hline 7 & 15.4 & \text { Standard Error } & 1.5055 &&\text { Standard Error } & 0.8155 \\\hline 5 & 13.9 & \text { Median } & 5.5 &&\text { Median } & 14.65 \\\hline 3 & 11.2 & \text { Mode } & 5 &&\text { Mode } & 13.9 \\\hline 19 & 18.7 & \text { Standard Deviation } & 4.7610 &&\text { Standard Deviation } & 2.5790 \\\hline 10 & 17.9 & \text { Sample Variance } & 22.6667 &&\text { Sample Variance } & 6.6511 \\\hline 8 & 16.8 & \text { Kurtosis } & 4.7702 &&\text { Kurtosis } & -1.1563 \\\hline 6 & 15.9 & \text { Skewness } & 2.0386 &&\text { Skewness } & 0.0535 \\\hline 3 & 11.5 & \text { Rarge } & 16 &&\text { Range } & 7.5 \\\hline 5 & 13.9 & \text { Minimum } & 3 &&\text { Minimum } & 11.2 \\\hline &&\text { Maximum } & 19 &&\text { Maximum } & 187 \\\hline &&\text { Sum } & 70 &&\text { Sum } & 148 \\\hline &&\text { Count } & 10 &&\text { Count } & 10 \\\hline\end{array}$ $\begin{array}{|l|c|c|c|c|c|c|}\hline \text { SUMMARY OUTPUT } & & \\\hline & & \\\hline \text { RegressionStatistics } & & \\\hline \text { Multiple R } & 0.8524 & \\\hline \text { RSquare } & 0.7267 & \\\hline \text { Adjusted R Square } & 0.6925 & \\\hline \text { Standard Error } & 1.4301 & \\\hline \text { Observations } & 10 & \\\hline & & \\\hline \text { ANOvA } & & & & & & \\\hline & d f & S S & \text { MS } & F & \text { significance } F & \\\hline \text { Regression } & 1 & 43.4982 & 43.4982 & 21.2682 & 0.0017 & \\\hline \text { Residual } & 8 & 16.3618 & 2.0452 & & & \\\hline \text { Total } & 9 & 59.8600 & & & & \\\hline & & \\\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \\\hline \text { Intercept } & 11.5676 & 0.8341 & 13.6579 & 0.0000 & 9.6441 & 13.4912 \\\hline \text { Number of vouchers } & 0.4618 & 0.1001 & 4.6117 & 0.0017 & 0.2309 & 0.6927 \\\hline\end{array}$ Determine the standard error of the estimate and describe what this statistic sells you about the regression line.