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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
34
45
9
92
16
90
25
132
36
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.
1+2+3+.....+n=1/2n(n+1)
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