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BMI; math portfolio type 2

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Introduction

Math portfolio SL type 2

Shiba Younus

IB 2

Katedralskolan

Date: 08-06-09

Body Mass Index

The table below gives the median BMI for females of different ages in the US in the year 2000.

Age (yrs)

BMI  

2

16.40

3

15.70

4

15.30

5

15.20

6

15.21

7

15.40

8

15.80

9

16.30

10

16.80

11

17.50

12

18.18

13

18.70

14

19.36

15

19.88

16

20.40

17

20.85

18

21.22

19

21.60

20

21.65

image00.png

Using graphmatica the data points were plotted on a graph:

image01.png

The BMI data provided is confined to females between 2-20 years of age in the US. No data for ages below 2 years or above 20 years is available. The variables age and BMI, as appear above, are along the x and y axes respectively.

Since the graph appears to resemble the curve of a polynomial function (studied earlier in the course) and since these functions are easier to work with algebraically, I decided to work with

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Middle

15.70= a33 + b32 + c3 + d…………...1 (x = 3, y = 15.70)

15.30 = a43 + b42 + c4 +d……….2 (x = 4, y = 15.30)

20.40 = a163 + b162 + c16 +d…….3 (x = 16, y = 20.40)

20.85 = a173 + b172 + c17 +d……...4 (x = 17, y = 20.85)

The answer from polysimultaneous equation solver was:

a = -0.00439

b = 0.164

c = -1.38

d = 18.5

So the model function is: y = -0.00439x3 + 0.164x2 - 1.38x + 18.5

image02.png

The model function fits the data points obediently.

Since the shape of the graph resembles the curve of a sine function too, therefore the sine regression function in the calculator was used to find another function that models the same data, and compared with the model function that was obtained algebraically: image03.png

Though the sine function shows a great deal of similarity in behaviour to the cubic function when it comes to fitting the data points, minor differences can be appreciated. There are noteworthy differences when it comes to y and x intersects of both functions. The y intersects for both functions differ by 0.

...read more.

Conclusion

2 + c(15) + d….4 (x = 15, y = 19.4)

The answer from polysimultaneous equation solver was:

a = -0.004, b = 0.15, c = -1.31, d = 17.9

The modified model function for this data is: y = -0.004x3 + 0.154x2 – 1.31x + 17.9

image07.png

The modified model function now appears to fit the graph of the data well.

Limitations to the model function are:

  1. The model function is obtained from a specific combination of variables (x, y) since other combinations result in different behaviours of the model function.
  2. It is unique for the particular range of age provided in the data. This implies that the BMI for ages outside that range cannot be correctly estimated. As seen in case of the 30-year-old woman in the US (fig 1.4).
  3. It cannot be applicable to BMI data for females from another country. The model function needs to be modified to fit the data points. As seen in fig 2.2

References: 1.http://www.massgeneral.org/children/adolescenthealth/articles/aa_body_mass_index.aspx

2. http://www.ijbs.org/User/ContentfullText.aspx?volumeNo=1&StartPage=57&Type=pdf

...read more.

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