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The Owner of an Air Conditioner Business Wants to Investigate

question 56

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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.  SUMMARY OUTPUT  Regression Statistics  Multiple R 0.99 R Square 0.97 Adjusted RSquare 0.96 Standard Error 4.54 Observations 14.00 ANOVA  df SSMSF Significance  Regression 4.006999.271749.8284.860.00 Residual 9.00185.5820.62 Total 13.007184.86 Coefficients  Standard  Error  tStat  P-value  Lower 95%  Upper 95% Intercept 17.948.542.100.0737.271.38 Temperature 1.000.352.840.020.201.79 March 1.014.600.220.839.3911.40 September 7.225.581.290.235.4019.84 Deomber 27.876.554.260.0013.0642.68\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 overall regression equation.

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Definitions:

SUTA Tax Rate

The state unemployment tax rate that employers pay to fund unemployment benefits, which can vary based on the employer's industry and experience with layoffs.

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