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MATH 1324 Finite Mathematics

tag 0 Download 4 Pages / 807 Words tag 06-11-2020


Predicting Body Fat Percentage


The Body(2).csv dataset is posted on the Assignment 3 website. It contains the percentage of body fat, age, weight, height, and ten body circumference measurements (e.g., abdomen) for a sample of 252 men and women.  Body fat, as measured using the Brozek method, is estimated through a time consuming underwater weighing technique to measure a person's density. Investigators want to determine if a general, easy to determine, body circumference measurement could be used as a general indicator for body fat percentage. If so, the investigators want to establish a formula that can convert a body circumference measurement to a predicted body fat percentage and also understand how well this prediction will hold. (original source: JSE-DA). The variables are as follows:


  1. Case: Case Number
  2. BFP_Brozek: Percent body fat using Brozek's equation, 457/Density - 414.2
  3. BFP_Siri: Percent body fat using Siri's equation, 495/Density - 450
  4. Density: Density (gm/cm3)
  5. Age: Age (yrs)
  6. Weight: Weight (lbs)
  7. Height: Height (inches)
  8. Adiposity_index: Adiposity index = Weight/Height2(kg/m2)
  9. Fat_free: Fat Free Weight  = (1 - fraction of body fat) * Weight, using Brozek's formula (lbs)
  10. Neck: Neck circumference (cm)
  11. Chest: Chest circumference (cm)
  12. Abdomen: Abdomen circumference (cm) "at the umbilicus and level with the iliac crest"
  13. Hip: Hip circumference (cm)
  14. Thigh: Thigh circumference (cm)
  15. Knee: Knee circumference (cm)
  16. Ankle: Ankle circumference (cm)
  17. Biceps: Extended biceps circumference (cm)
  18. Forearm: Forearm circumference (cm)
  19. Wrist: Wrist circumference (cm) "distal to the styloid processes"
  20. Sex: “1” for male and “0” for female

The Assignment

  • Test whether the mean body fat percentage for males and females are the same. Write down your null and alternative hypothesis clearly, express your conclusion in words and provide your reason(s) for your final conclusion.
  • Estimate the 99% confidence interval for the mean body fat percentage in the population. Is there any assumption for the body fat percentage distribution that we need to investigate? Explain your reason (s).
  • Researchers believe that average body fat percentage is less than 12.5. Test this claim. Write down your null and alternative hypothesis clearly, express your conclusion in words and provide reason(s) for your final conclusion.
  • Find the single best predictor of body fat percentage (Brozek method) using the body circumference data. Write a report that explains your method for identifying the single best predictor. Use the best predictor to determine a model that can convert a person’s body circumference measurement to an estimated body fat percentage. Ensure you test the model parameters and any assumptions. Critique the predictive ability of the model and draw an overall conclusion to help the investigators
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