A Company Selling Swimming Goggles Wants to Analyze Its Australian

question 44

Essay

A company selling swimming goggles wants to analyze its Australian sales figures.
Time series forecasting with regression was used to generate Excel output to estimate trend and seasonal effects of the time series of Swimming goggle sales (in thousands of dollars) where the origin is the March Quarter 2000 and Q1 denotes sales in the March quarter, Q3 denotes sales in the September quarter and Q4 denotes sales in the December quarter. $\begin{array}{l}\text { SUMMARV OUTPUT }\\\hline\text { Regression Stotitics }\\\begin{array}{lc}\hline \text { Multiple R } & 0.9460 \\\text { R Square } & 0.8950 \\\text { Adjusted RSquare } & 0.8864 \\\text { Standard Error } & 3.7394 \\\text { Observations } & 54 \\\hline\end{array}\end{array}$
$\text { ANOVA }$
$\begin{array}{lccccc} \hline& & & & & \text { Sgnificance } \\& d f & S & M S & F & F \\\hline \text { Regression } & 4 & 5837.596003 & 1459.4 & 104.3701 & 2.41949 \mathrm{E}-23 \\\text { Residual } & 49 & 685.1632564 & 13.9829 & & \\\text { Total } & 53 & 6522.759259 & & &\\\hline\end{array}$
$\begin{array}{lcrrrrr}\hline&& \text { Standard } & & && \text { Upper } \\&\text { Coefficients } & \text { Error } & \text { t Stat } & \text {p-value } & \text { Lower } 95 \%& 95 \%\\\hline\text { Intercept } & 3.0588 & 1.3331 & 2.2944 & 0.0261 & 0.3797 & 5.7378 \\\mathrm{t} & 0.2518 & 0.0327 & 7.7052 & 0.0000 & 0.1861 & 0.3175 \\\mathrm{Q} 1 & 12.4604 & 1.3897 & 8.9664 & 0.0000 & 9.6677 & 15.2530 \\\mathrm{Q} 3 & 1.1458 & 1.4721 & 0.7784 & 0.4401 & -1.8124 & 4.1041 \\\mathrm{Q} 4 & 23.9121 & 1.4403 & 16.6025 & 0.0000 & 21.0177 & 26.8064\\\hline\end{array}$ (a) Write out the regression equations for each of the four quarters.
(b) Sketch the four equations from part (a) on the same set of axes.
(c) Interpret the coefficients on all the indicator variables.
(c) All the indicator variables have positive coefficients. Is this surprising? Explain.

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