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Linear Models : Choosing Between Point-Slope, Slope-Intercept and Standard Forms

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Find an example, of the BMI between man/woman and estimate a best fit line graphically. Develop an approximate linear model using the point slope form, the slope-intercept form or the standard form line. You are not to graph the line here but help illustrate your point . You are only required to use the line of the forms to identify it (write the equation) and describe important features about it. Explain why you chose your form and the benefits of that form over the other two. Show how predictions might be made using your model .

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Solution Summary

A line form is chosen to model BMI (body mass index).The expert shows how prediction might be made using your model. The solution is detailed.

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This paper examines the relationships between BMI and body composition in different populations where low BMIs might be expected. The extent to which low BMIs are influenced by differences in size and shape is also assessed. There are meagre data on BMI and measured body composition in Third World populations and the more voluminous data are indirect. The paper concludes with a description of the contribution of variations in shape to BMI differences within and between populations.

BMI and body composition: theoretical considerations

In the first instance, the relationship between BMI and body composition can be modelled. Figure 1 shows the relationship when weight of varying composition is added or subtracted to a 70 kg man of stature 1.75 m, i.e. with a BMI of 22.9kg/m: and an assumed % fat of 15%. The relationship is non-linear and the slope decreases as the proportion of fat in the weight difference falls. The BMI at 0% fat varies too, ranging from 10 to 20kg/m2. There is an equally wide range in % fat at high or low BMI. In a 60 kg woman, stature 1.625 m, BMI 22.7 kg/m2 and % fat 25%, a similar pattern emerges except that at a weight change with 25% fat being deposited or lost, the line is horizontal. However, most investigators find the empirical relationship between BMI and % fat to be linear or almost so.

Forbes (1987) has suggested that the composition of tissue lost or gained varies according to the initial level of fatness. There is less fat in the tissue change at lower levels of initial fatness. This was based on the differences of 164 women of widely differing composition but of stature ...

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