The sales data for a consumer item is shown below for year 2004.
| Month |
Sales (Rs in
' 000) |
| Jan |
21.6 |
| Feb |
22.9 |
| Mar |
25.5 |
| Apr |
21.9 |
| May |
23.9 |
| Jun |
27.5 |
| July |
31.5 |
| Aug |
29.7 |
| Sep |
28.6 |
| Oct |
31.4 |
|
Using linear regression method, estimate the
sales for the month of Nov.
Let us indicate month as t and Sales in a month 't' as Yt
Let us relabel months Jan to Oct as 1,2.. up to 10.
The form of the regression equation is
Yt = a + b t
| T |
Yt |
tYt |
t2 |
| 1 |
21.6 |
21.6 |
1 |
| 2 |
22.9 |
45.8 |
4 |
| 3 |
25.5 |
76.5 |
9 |
| 4 |
21.9 |
87.6 |
16 |
| 5 |
23.9 |
119.5 |
25 |
| 6 |
27.5 |
165.0 |
36 |
| 7 |
31.5 |
220.5 |
49 |
| 8 |
29.7 |
237.6 |
64 |
| 9 |
28.6 |
257.4 |
81 |
| 10 |
31.4 |
257.4 |
100 |
| Totals |
|
|
|
| 55 |
264.5 |
1545.5 |
385 |
|
tbar = 55/10=5.5
Ybar = 264.5/10=26.45
The coefficient in regression equation
b = (? t Yt - ?t ?Yt )/n / (?t2 - (?t)2)/n
= (1545.5 - 55 x 264.5)/10 / (385- 552)/10
= 90.75/82.5 = 1.1
a = Ybar -(b) tbar =26.45 - 1.1 x 5.5 = 20.4
Therefore the regression equation is
Yt = 20.4 + 1.1 t
Using the above equation, the forecast for November (t=11) and
December (t=12) shall be in (thousands of rupees)
Y (Nov) = 20.4 + 1.1 x 11 = 32.4
Y (Dec) = 20.4 + 1.1 x 12 = 33.6
|
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