## Forecasting by using least squares, Mathematics

Assignment Help:

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.

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