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Broadband

x. y (000s). 0 110. 1 200. 2 370. 3 830. 4 1500. 5 2730. 6 3200. Broadband. Number of connections at 6 monthly intervals from Jan 1 st 2001. 2. a = 91. 3. 2. The quadratic model is y = 91 x 2 - 35 x + 110. 3. To find a quadratic model.

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Broadband

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

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

  3. 2 91 3 Quadratic model: y = x2- 35x + 110 % Error y (000s) data y (000s) model Broadband x 110 0% 0 110 1 200 167 - 17% 2 370 407 10% 830 0% 3 830 1437 - 4% 4 1500 5 2730 2227 - 6% 6 3200 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 • a graph Compare values predicted by the model with the actual data using • % 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.

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