Forecasting by using least squares, Mathematics

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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 8^th 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 8^th year sales = 12 + 1.86 (8)

=26.88 that is 26,888 units.

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