A Company Selling Swimming Goggles Wants to Analyze Its Australian

question 125

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) Forecast swimming goggle sales for all four quarters of 2016.
(b) Are these good forecasts? Explain.
(c) Separate the difference in your forecasts for June 2016 and December 2016 between seasonal and trend.

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Definitions:

Municipal Bond

A debt security issued by a city, municipality, or county to finance its capital expenditures, often offering tax-free interest payments to investors.

Municipal Bond

A debt security issued by a state, municipality, or county to finance its capital expenditures, often tax-exempt for investors.

Marginal Tax Bracket

The tax rate that applies to the next dollar of taxable income, indicating the percentage of tax paid on the last dollar earned.

Taxable Yield

The yield on an investment before the effects of taxes are taken into account, relevant for investors in taxable accounts.