The Owner of an Air Conditioner Business Wants to Investigate

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.