1 / 5

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.

xyla-thomas
Télécharger la présentation

Broadband

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related