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A Company Selling Swimming Goggles Wants to Analyze Its Australian

Question 116

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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 Obserwations 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 { Obserwations } & 54 \\\hline\end{array}\end{array}
ANOVA
dfSS MS F Significance  Regression 45837.5960031459.4104.37012.41949E23 Residual 49685.163256413.9829 Total 536522.759259\begin{array}{lccccc}\hline & d f & S S & \text { MS } & F & \text { Significance } \\\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) Using p-values test the significance of the independent variables.
(b) Test the significance of the overall regression equation.

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(a) Ho: βt = 0
HA: βt ≠ 0 p-value = 0, so t...

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