The Owner of an Air Conditioner Business Wants to Investigate

question 82

Short Answer

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. $\begin{array}{|l|r|r|r|r|r|c|}\hline \text { SUMMARY OUTPUT } & \\\hline \text { Regression Statistics } & \\\hline \text { Multiple R } & 0.99 \\\hline \text { R Square } & 0.97 \\\hline \text { Adjusted RSquare } & 0.96 \\\hline \text { Standard Error } & 4.54 \\\hline \text { Observations } & 14.00 \\\hline\\\hline \text { ANOVA }\\\hline &{\text { df }} &{SS} &MS & F& {\text { Significance }} \\\hline \text { Regression } & 4.00 & 6999.27 & 1749.82 & 84.86 & 0.00 \\\hline \text { Residual } & 9.00 & 185.58 & 20.62 & & \\\hline \text { Total } & 13.00 & 7184.86 & & & \\\hline\\\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \begin{array}{c}\text { Upper } \\95 \%\end{array} \\\hline \text { Intercept } & -17.94 & 8.54 & -2.10 & 0.07 & -37.27 & 1.38 \\\hline \text { Temperature } & 1.00 & 0.35 & 2.84 & 0.02 & 0.20 & 1.79 \\\hline \text { March } & 1.01 & 4.60 & 0.22 & 0.83 & -9.39 & 11.40 \\\hline \text { September } & 7.22 & 5.58 & 1.29 & 0.23 & -5.40 & 19.84 \\\hline \text { Deomber } & 27.87 & 6.55 & 4.26 & 0.00 & 13.06 & 42.68 \\\hline\end{array}$ Using the p-values from Excel, state which of the quarters are statistically significant at α of 5%.

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