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A Company Selling Swimming Goggles Wants to Analyze Its Australian

question 36

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
 Regression Statistios  Multiple R 0.9460 R Square 0.8950 Adjusted R Square 0.8864 Standard Error 3.7394 Observations 54\begin{array}{l}\text { Regression Statistios }\\\begin{array}{lc}\hline \text { Multiple R } & 0.9460 \\\text { R Square } & 0.8950 \\\text { Adjusted R Square } & 0.8864 \\\text { Standard Error } & 3.7394 \\\text { Observations } & 54 \\\hline\end{array}\end{array}

ANOVA
 Significance dfSS MS FF Regression 45837.5960031459.4104.37012.41949E23 Residual 49685.163256413.9829 Total 536522.759259\begin{array}{lccccc} & & & & & \text { Significance } \\& 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}

Standard Upper  Coeffcients  Error  t Stat  P-value  Lower 95%95% Intercept 3.05881.33312.29440.02610.37975.7378t0.25180.03277.70520.00000.18610.3175Q112.46041.38978.96640.00009.667715.2530Q31.14581.47210.77840.44011.81244.1041Q423.91211.440316.60250.000021.017726.8064\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) 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:

Intrauterine Devices (IUDs)

Long-term, reversible contraceptives inserted into the uterus to prevent pregnancy, available in hormonal and non-hormonal forms.

Cervical Mucus

A fluid secreted by the cervix, undergoing changes in consistency and volume across the menstrual cycle, playing a key role in fertility.

Spermicidal Agent

A chemical product used to kill sperm, thereby reducing the likelihood of pregnancy.

Diaphragm

A barrier method of contraception, consisting of a dome-shaped cup made of silicone or latex that fits inside the vagina to cover the cervix and prevent sperm from entering.

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