The Manager of a Fast Food Restaurant Wants to Determine

question 111

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. $$\begin{array} { | c | c | } \hline \text { Number of vouchers } & \text { Sales } \\\hline 4 & 12.8 \\\hline 7 & 15.4 \\\hline 5 & 13.9 \\\hline 3 & 11.2 \\\hline 19 & 18.7 \\\hline 10 & 17.9 \\\hline 8 & 16.8 \\\hline 6 & 15.9 \\\hline 3 & 11.5 \\\hline 5 & 13.9 \\\hline\end{array}$$ $\begin{array}{|l|c|c|c|c|c|c|}\hline \text { SUMMARY OUTPUT }\\\hline \text { Regression Statistics } & \\\hline \text { Multiple R } & 0.8524 \\\hline \text { R Square } & 0.7267 \\\hline \text { Adjuted R Square } & 0.6925 \\\hline \text { Standard Error } & 1.4301 \\\hline \text { Observations } & 10.0000 \\\hline\\\hline\text { ANOVA }\\\hline & & & & & \text { Sgnificance } \\& d f & S S & M S & F & F \\\hline \text { Regression } & 1.0000 & 43.4982 & 43.4982 & 21.2682 & 0.0017 \\\hline \text { Residual } & 8.0000 & 16.3618 & 2.0452 & & \\\hline \text { Total } & 9.0000 & 59.8600 & & & \\\hline\\\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \begin{array}{c}\text { Upper } \\95 \%\end{array} \\\hline \text { Interoept } & 11.5676 & 0.8341 & 13.8679 & 0.0000 & 9.6441 & 13.4912 \\\hline \text { Number of voudhers } & 0.4618 & 0.1001 & 4.6117 & 0.0017 & 0.2309 & 0.6927 \\\hline\end{array}$ Interpret the coefficient of determination.

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Definitions:

Warm Receptors

Sensory receptors in the skin that detect increases in temperature, contributing to the sensation of warmth.

Nociceptor

A sensory receptor that responds to damaging or potentially damaging stimuli by sending signals to the spinal cord and brain.

Thermoreceptor

A type of sensory receptor specialized to detect changes in temperature.

Meissner's Corpuscles

Specialized nerve endings in the skin that are sensitive to light touch and texture.