The Owner of an Air Conditioner Business Wants to Investigate

question 91

Essay

The owner of an air conditioner business wants to investigate the relationship between the weekly number of air conditioners sold with average weekly temperature and the seasons of the year.
A random sample of 14 weeks is taken, with the average temperature of that week (in degrees Celsius) and the quarter from which that week belonged, noted.
There are three indicator variables: March, September and December.
Excel is used to generate the following multiple linear regression output. $\begin{array}{|l|r|r|r|r|r|c|}\hline \text { SUMMARY OUTPUT } & \\\hline \text { Regression Statistics } & \\\hline \text { Multiple R } & 0.99 \\\hline \text { R Square } & 0.97 \\\hline \text { Adjusted RSquare } & 0.96 \\\hline \text { Standard Error } & 4.54 \\\hline \text { Observations } & 14.00 \\\hline\\\hline \text { ANOVA }\\\hline &{\text { df }} &{SS} &MS & F& {\text { Significance }} \\\hline \text { Regression } & 4.00 & 6999.27 & 1749.82 & 84.86 & 0.00 \\\hline \text { Residual } & 9.00 & 185.58 & 20.62 & & \\\hline \text { Total } & 13.00 & 7184.86 & & & \\\hline\\\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \begin{array}{c}\text { Upper } \\95 \%\end{array} \\\hline \text { Intercept } & -17.94 & 8.54 & -2.10 & 0.07 & -37.27 & 1.38 \\\hline \text { Temperature } & 1.00 & 0.35 & 2.84 & 0.02 & 0.20 & 1.79 \\\hline \text { March } & 1.01 & 4.60 & 0.22 & 0.83 & -9.39 & 11.40 \\\hline \text { September } & 7.22 & 5.58 & 1.29 & 0.23 & -5.40 & 19.84 \\\hline \text { Deomber } & 27.87 & 6.55 & 4.26 & 0.00 & 13.06 & 42.68 \\\hline\end{array}$ Test the significance of the coefficient of Temperature, at the 5% level of α. Justify your choice of the alternative hypothesis.

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Definitions:

Business Principles

Fundamental guidelines or rules that are used to conduct business activities and decisions ethically and effectively.

Role Playing

A technique in therapy or training where individuals assume roles and act them out in scenarios, to explore behavior, practice social skills or gain insight.

Cognitive-Behavioral Therapy

A therapeutic method aimed at tackling ineffective emotions, actions, and thoughts via a deliberate, goal-focused procedure.

Maladaptive Assumptions

Irrational beliefs or thought patterns that are resistant to change and can lead to negative emotions, behaviors, and mental health outcomes.