Forecasting By Using Least Squares
Data have been kept of sales over the last seven years
|
Year
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
Sales (in '000 units
|
14
|
17
|
15
|
23
|
18
|
22
|
27
|
|
It is required to forecast the sales for the 8th year
|
Solution
|
Years (x)
|
Sales (y)
|
xy
|
x2
|
|
1
|
14
|
14
|
1
|
|
2
|
17
|
34
|
4
|
|
3
|
15
|
45
|
9
|
|
4
|
23
|
92
|
16
|
|
5
|
18
|
90
|
25
|
|
6
|
22
|
132
|
36
|
|
7
|
27
|
189
|
49
|
|
Σx=28
|
Σy = 136
|
Σxy=596
|
Σx2= 140
|
136 = 7a + 28b
596 = 28a + 140b
∴b = 1.86
And substituting in one of the equations we acquire
a = 12
∴ Regression line = y = 12 + 1.86x
Or, Sales in ('000s of units) = 12.00 + 1.86 (no of years)
We utilize this expression for forecasting, for 8th year sales = 12 + 1.86 (8)
=26.88 that is 26,888 units.