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. (Negative answers should be indicated by minus sign. Round your answers to 3 decimal places.)

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.

Explanation / Answer

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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