Homework SourseAppliance Center sells a variety of electronic equipment and
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 |
Solution
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 |
