Broadband Number of connections at 6 monthly intervals from Jan 1st 2001 0 110 1 200 2 370 3 830 4 1500 y (000s) x 5 2730.

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Broadband Number of connections at 6 monthly intervals from Jan 1st 2001 0 110 1 200 2 370 3 830 4 1500 y (000s) x 5 2730 6 3200

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

Quadratic model: y = x2 - 35x + 110 Broadband Quadratic model: y = x2 - 35x + 110 91 2 3 x y (000s) data y (000s) model % Error 0 110 110 0% 1 200 167 - 17% 2 370 407 10% 3 830 830 0% 4 1500 1437 - 4% 5 2730 2227 - 6% 6 3200 3200 0% Value predicted by model – Actual Value ´ 100 % Error = Actual Value

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

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.