Appliance Center sells a variety of electronic equipment and home appliances. Fo

Question

Appliance Center sells a variety of electronic equipment and home appliances. For the last 4 years, 2010 through 2013, the following quarterly sales (in $ millions) were reported.

Use the seasonal indexes you computed to determine the deseasonalized sales. Determine the linear trend equation based on the quarterly data for the 4 years. Forecast the seasonally adjusted sales for 2014. (Round your answers to 3 decimal places.)

Quarter Year I II III IV 2010 5.3 4.1 6.8 6.7 2011 4.8 3.8 5.6 6.8 2012 4.3 3.8 5.7 6.0 2013 5.6 4.6 6.4 5.9 Appliance Center sells a variety of electronic equipment and home appliances. For the last 4 years, 2010 through 2013, the following quarterly sales (in $ millions) were reported. Quarter Year I II III IV 2010 5.3 4.1 6.8 6.7 2011 4.8 3.8 5.6 6.8 2012 4.3 3.8 5.7 6.0 2013 5.6 4.6 6.4 5.9 Use the seasonal indexes you computed to determine the deseasonalized sales. Determine the linear trend equation based on the quarterly data for the 4 years. Forecast the seasonally adjusted sales for 2014. (Round your answers to 3 decimal places.) Y hat = _____+ _____t Fitted Index Forecast _______ 0.907 _____ _______ 0.760 _____ _______ 1.126 _____ _______ 1.209 _____

Explanation / Answer

xplanation

We will find an equation of the regression line in 4 steps.

Step 1: Find X?Y and X2 as it was done in the table below.

Step 2: Find the sum of every column:

?X=136 , ?Y=86.2 , ?X?Y=740.1 , ?X2=1496

Step 3: Use the following equations to find a and b:

ab=?Y??X2??X??XYn??X2?(?X)2=86.2?1496?136?740.116?1496?1362?5.203=n??XY??X??Yn??X2?(?X)2=16?740.1?136?86.216?1496?(136)2?0.022

Step 4: Substitute a and b in regression equation formula

y y = a + b?x= 5.203 + 0.022?x

Note:I quarter starting is taken as 1, then 2 etc.

y = 5.203+0.022x

X Y X?Y X?X 1 5.3 5.3 1 2 4.1 8.2 4 3 6.8 20.4 9 4 6.7 26.8 16 5 4.8 24 25 6 3.8 22.8 36 7 5.6 39.2 49 8 6.8 54.4 64 9 4.3 38.7 81 10 3.8 38 100 11 5.7 62.7 121 12 6.0 72 144 13 5.6 72.8 169 14 4.6 64.4 196 15 6.4 96 225 16 5.9 94.4 256

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