A Company Selling Swimming Goggles Wants to Analyze Its Australian

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. SUMMARY OUTPUT
$\begin{array}{lc}\text { Regression Statistios } & \\\hline \text { Multiple R } & 0.9460 \\\text { R Square } & 0.8950 \\\text { Adjusted R Square } & 0.8864 \\\text { Standard Error } & 3.7394 \\\text { obseruations } & 54 \\\hline\end{array}$
ANOVA
$\begin{array}{l}\begin{array} { l c r r r r } &&&&&\text { Signficance }\\& d f & S S & \text { MS } & F & F \\\hline \text { Regression } & 4 & 5837.596003 & 1459.4 & 104.3701 & 2.41949 \mathrm { E } - 23 \\\text { Residual } & 49 & 685.1632564 & 13.9829 & & \\\text { Total } & 53 & 6522.759259 & & & \\\hline\end{array}\end{array}$


$\begin{array}{lcccccr} && \text {Standard }&&&& \text {Upper }\\& \text { Coeffcients } & \text { Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & 95 \% \\\hline \text { Intercept } & 3.0588 & 1.3331 & 2.2944 & 0.0261 & 0.3797 & 5.7378 \\\mathrm{t} & 0.2518 & 0.0327 & 7.7052 & 0.0000 & 0.1861 & 0.3175 \\\mathrm{Q} 1 & 12.4604 & 1.3897 & 8.9664 & 0.0000 & 9.6677 & 15.2530 \\\mathrm{Q} 3 & 1.1458 & 1.4721 & 0.7784 & 0.4401 & -1.8124 & 4.1041 \\\mathrm{Q4} & 23.9121 & 1.4403 & 16.6025 & 0.0000 & 21.0177 & 26.8064\end{array}$ (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.