The Owner of an Air Conditioner Business Wants to Investigate

question 5

Essay

The owner of an air conditioner business wants to investigate the relationship between the weekly number of air conditioners sold, 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. $\begin{array}{|l|r|r|r|r|r|c|}\hline \text { SUMMARY OUTPUT } & \\\hline \text { Regression Statistics } & \\\hline \text { Multiple R } & 0.99 \\\hline \text { R Square } & 0.97 \\\hline \text { Adjusted RSquare } & 0.96 \\\hline \text { Standard Error } & 4.54 \\\hline \text { Observations } & 14.00 \\\hline\\\hline \text { ANOVA }\\\hline &{\text { df }} &{SS} &MS & F& {\text { Significance }} \\\hline \text { Regression } & 4.00 & 6999.27 & 1749.82 & 84.86 & 0.00 \\\hline \text { Residual } & 9.00 & 185.58 & 20.62 & & \\\hline \text { Total } & 13.00 & 7184.86 & & & \\\hline\\\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \begin{array}{c}\text { Upper } \\95 \%\end{array} \\\hline \text { Intercept } & -17.94 & 8.54 & -2.10 & 0.07 & -37.27 & 1.38 \\\hline \text { Temperature } & 1.00 & 0.35 & 2.84 & 0.02 & 0.20 & 1.79 \\\hline \text { March } & 1.01 & 4.60 & 0.22 & 0.83 & -9.39 & 11.40 \\\hline \text { September } & 7.22 & 5.58 & 1.29 & 0.23 & -5.40 & 19.84 \\\hline \text { Deomber } & 27.87 & 6.55 & 4.26 & 0.00 & 13.06 & 42.68 \\\hline\end{array}$ (a) Write the linear regression model for each quarter: March, June, September and December
(a) Roughly, sketch on the same set of axes, showing the intercept and the slope.

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Definitions:

Preferred Activity

An activity that an individual chooses or prefers over other options, often used in reinforcement learning and behavior modification strategies.

Response Deprivation Theory

A theory suggesting that a behavior can become reinforcing when access to that behavior is restricted below its baseline level of occurrence.

Baseline Occurrence

The rate at which a behavior occurs before any intervention or conditioning is applied.

Probability-Differential Theory

The idea that an activity will have reinforcing properties when its probability of occurrence is greater than that of the reinforced activity.