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 8^{th} year
Solution
Years (x)
Sales (y)
xy
x^{2}
34
45
9
92
16
90
25
132
36
189
49
Σx=28
Σy = 136
Σxy=596
Σx^{2}= 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 8^{th} year sales = 12 + 1.86 (8)
=26.88 that is 26,888 units.