Suppose you ran the following regression model, where the dependent variable is

Question

Suppose you ran the following regression model, where the dependent variable is the bone mineral density of the femoral neck. Your independent variables are the percentage of body fat, weight, activity level and an interaction between the percentage of body fat and weight. You also calculate the variance inflation factor for each variable in the model

A) What type of problem (if any) do you observe with this model?

B) What would your next steps be as a researcher, and what information should you convey to your reader?

Explanation / Answer

1. Introduction of Body Density data.

This is a comprehensive dataset that lists estimates of the percentage of body fat determined by underwater weighing and various body circumference measurements for 252 men. These data were generously supplied by Dr. A. Garth Fisher who gave permission to freely distribute the data and use for non-commercial purposes. These data are used to produce the predictive equations for lean body weight given in the abstract Generalized body composition prediction equation for men using simple measurement techniques, K.W. Penrose, A.G. Nelson, A.G. Fisher, FACSM, Human Performance Research Center, Brigham Young University, Provo, Utah 84602 as listed in Medicine and Science in Sports and Exercise, vol. 17, no. 2, April 1985, p. 189.(http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_BMI_Regression#References)

2. Theories about BMI and Body Fat Percentage

Some experts tout BMI(body mass index) as the most accurate and simple way to determine the effect of weight on your health. In fact, most recent medical research uses BMI as an indicator of someone’s health status and disease risk. Some debate about which values on the BMI scale the thresholds for ‘underweight’, ‘overweight’ and ‘obese’ should be set. However, the followings are used for the criteria.(http://healthiack.com/body-fat-percentage-calculator)
BMI < 18.5 : underweight,
18.5 < BMI < 25 : optimal weight,
25 < BMI < 30 : overweight,
BMI > 30 : obese.

Meanwhile, in September 2000, the American Journal of Clinical Nutrition published a study showing that body-fat percentage may be a better measure of your risk of weight-related diseases than BMI.(http://www.webmd.com/diet/body-fat-measurement). Percentage of body fat for an individual can be estimated by the Siri’s formula(1956) once body density has been determined. The American Council on Exercise provides the following ranges for men’s body-fat percentage:

essential fat : 2-5%
athletes : 6-13%
fitness : 14-17%
Normal : 18-24%
obese : more than 24%

3. The variables of Body Density data.

The body density dataset includes the following 15 variables listed from left to right:
Density : Density determined from underwater weighing
Fat : Percent body fat from Siri’s (1956) equation
Age : Age (years)
Weight : Weight (kg)
Height : Height (cm)
Neck : Neck circumference (cm)
Chest: Chest circumference (cm)
Abdomen : Abdomen circumference (cm)
Hip : Hip circumference (cm)
Thigh : Thigh circumference (cm)
Knee : Knee circumference (cm)
Ankle : Ankle circumference (cm)
Biceps : Biceps (extended) circumference (cm)
Forearm : Forearm circumference (cm)
Wrist : Wrist circumference (cm)

New variable MassIndex will be created as the ratio of Weight(kg) to Height(m) squared for the measure of Body Mass Index in addition to the above variables. Model Selection process and regressions for both response variables, Fat and MassIndex, will be compared to explain which measure explains this data better.

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