1. Broadband
Number of connections at 6 monthly intervals from Jan 1st 2001
y (000s) x

2. To find a quadratic model y = ax2 + bx + c
Using 3 points:
(0, 110)
(3, 830)
(6, 3200)
gives:
110 = c
Substituting for c:
830 = 9a + 3b + c
830 = 9a + 3b + 110
3200 = 36a + 6b + c
3200 = 36a + 6b + 110
Simplifying:
9a + 3b = 720
3a + b = 240 (1)
36a + 6b = 3090
6a + b = 515 (2)
a = 91 2 3
Subtracting (2) – (1): 3a
= 275
Substituting for a in (1):
275 + b = 240
b = - 35
The quadratic model is y = 91 x2 - 35x + 110 2 3

3. Quadratic model: y = x2 - 35x + 110
Broadband
Quadratic model: y = x2 - 35x + 110 91 2 3 x
y (000s) data
y (000s) model
% Error
110 0%
167
- 17%
407
10%
830 0%
1437
- 4%
2227
- 6%
3200 0%
Value predicted by model – Actual Value
´ 100
% Error =
Actual Value

4. Use a graph to compare the predictions from the model with the data:

5. Evaluating the model
Compare values predicted by the model with the actual data using
a graph
% errors
Compare with models found using
different points
Excel
a graphic calculator
In general:
the more data that is used, the better the model is likely to be
predictions of future values become less reliable, the further they are from the data used to find the model.