The Manager of a Fast Food Restaurant Wants to Determine

question 173

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. $$\begin{array} { | c | c | } \hline \text { Number of vouchers } & \text { Sales } \\\hline 4 & 12.8 \\\hline 7 & 15.4 \\\hline 5 & 13.9 \\\hline 3 & 11.2 \\\hline 19 & 18.7 \\\hline 10 & 17.9 \\\hline 8 & 16.8 \\\hline 6 & 15.9 \\\hline 3 & 11.5 \\\hline 5 & 13.9 \\\hline\end{array}$$ $\begin{array}{|l|c|c|c|c|c|l|}\hline \text { SUMMARY OUTPUT } & \\\hline & \\\hline \text { Regression Statistics } & \\\hline \text { Multiple R } & 0.8524 \\\hline \text { R Square } & 0.7267 \\\hline \text { Adjusted R Square } & 0.6925 \\\hline \text { Standard Error } & 1.4301 \\\hline \text { Observations } & 10 \\\hline & \\\hline \text { ANOvA } & & & & & & \\\hline & d f & S S & M S & F & \text { Significance } F & \\\hline \text { Regression } & 1 & 43.4982 & 43.4982 & 21.2682 & 0.0017 & \\\hline \text { Residual } & 8 & 16.3618 & 2.0452 & & & \\\hline \text { Total } & 9 & 59.8600 & & & & \\\hline\\\hline & \text { Coeficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & t \text { Stat } & \text { P-value } & \text { Lower } 95 \% & \begin{array}{c}\text { Upper } \\95 \%\end{array} \\\hline \text { Intercept } & 11.5676 & 0.8341 & 13.8679 & 0.0000 & 9.6441 & 13.4912 \\\hline \text { Number of vouchers } & 0.4618 & 0.1001 & 4.6117 & 0.0017 & 0.2309 & 0.6927 \\\hline\end{array}$ a. Write down the regression equation
b. Interpret the slope.

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Definitions:

Database

An organized collection of structured information or data, typically stored electronically in a computer system.

Object-oriented

A programming paradigm based on the concept of "objects", which can contain data, in the form of fields, and code, in the form of procedures, making software design more modular.

Relational

Pertaining to databases in which data is organically structured in table form, emphasizing relations between different entities and variables.

Referential Integrity

In a relational database, a condition where, for each value in the foreign key table, there’s a corresponding value in the primary key table.