The Manager of a Fast Food Restaurant Wants to Determine

question 102

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 the predicted sales.
Calculate the residuals. $$\begin{array} { | c | c | c | c | } \hline \text { Observation } & \text { Sales } & \text { Predicted Sales } & \text { Residuals } \\\hline 1 & 12.8 & 13.4147 & - 0.6147 \\\hline 2 & 15.4 & 14.8000 & 0.6000 \\\hline 3 & 13.9 & 13.8765 & 0.0235 \\\hline 4 & 11.2 & 12.9529 & - 1.7529 \\\hline 5 & 18.7 & 20.3412 & - 1.6412 \\\hline 6 & 17.9 & 16.1853 & 1.7147 \\\hline 7 & 16.8 & 15.2618 & 1.5382 \\\hline 8 & 15.9 & 14.3382 & 1.5618 \\\hline 9 & 11.5 & 12.9529 & - 1.4529 \\\hline 10 & 13.9 & 13.8765 & 0.0235 \\\hline\end{array}$$ Plot the residuals against the predicted values of y. Does the variance appear to be constant?

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Definitions:

Physical Responses

Bodily reactions to stimuli, including stress, excitement, or environmental changes.

Emotional Responses

The feelings or emotions that are elicited in an individual as a reaction to stimuli or situations.

Muscle Tension

Physical discomfort or strain in the muscles, often resulting from stress, overuse, or underlying health conditions, that can lead to pain and stiffness.

Burnout

A psychological syndrome emerging as a prolonged response to chronic interpersonal stressors on the job, characterized by exhaustion, cynicism, and a feeling of reduced professional efficacy.