Forecasting by using least squares, Mathematics

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.

Posted Date: 2/16/2013 7:49:36 AM | Location : United States







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