Linear Regression Forecast
Nicolas Scott Gomez
Park University

Introduction………………………………………………………………………………………..3
Subjects and Methods...…………………..…………………………….…………………………3
Results…………………..…………………………………………………………………………4
References…...…………………………………………………………………………………….7

Introduction
There is a growing awareness of obesity in more modern nations which has added importance to efforts in understanding causes and natural history of obesity. In order to understand it, you must determine what a normal body fat content is and how it changes with age. Most recently, there are four component models of body composition that don’t rely on major assumptions about constant compositions that have been developed. The models offer the opportunity to determine the relation between age and body composition components such as fat in a more accurate way. In 1999, a study was done showing several studies showing body composition variables like fat mass and how they vary significantly among ethnic groups.
Subjects and Methods
Fat mass was determined once in a large sample of healthy volunteers by using a 4 component model requiring measurement of body volume, total body water, total body bone mineral mass and the body weight. The relation between age and body fat was explored by using several different statistical methods and the 1324 volunteers ages 20-94 were recruited for his study through various means of advertising. These studies were performed between 1986 and 1997 and each potential subject needed to have all four grandparents while also being screened with a medical history questionnaire and brief physical exam.
Each subject fasted overnight and a body weight was measured to + 0.2 kg by using a standard balance scale and measured to + 0.5 cm and all the measurements were completed on the same day.
Body density and volume were determined by using a specific method where each subject wore a bathing suit and performed 5-10 submersions with maximum exhalations. Total body fat was calculated in all subjects by using a 4 component model requiring measurements of body volume, TBW, TBBM and body weight. This method provides estimates of body fat that are independent of major age, sex and ethnicity related assumptions by using the equation: Fat mass = (2.513 x body volume) – (.739 x TBW) + (.947 x TBBM) – (1.79 x body weight). This equation is estimated to be 1.6% of body weight.
Subjects were also divided into age groups by decade and the mean and standard deviation of fat mass and fat percentage for each age group were calculated. The linear regression analysis was also performed independently for each ethnic and sex group and coefficients were compared across groups and for fat mass, this analysis was performed both with and without adjustment for body size.
Results
Number of subjects by age, sex, and ethnicity | | Age | | 20–29 y | 30–39 y | 40–49 y | 50–59 y | 60–69 y | 70–79 y | ≥80 y | All ages | Women | | | | | | | | | Asian | 17 | 22 | 16 | 21 | 31 | 9 | 4 | 120 | Black | 16 | 36 | 31 | 31 | 27 | 15 | 6 | 162 | Puerto Rican | 17 | 19 | 15 | 25 | 15 | 6 | 1 | 98 | White | 56 | 73 | 47 | 70 | 55 | 44 | 15 | 360 | Men | | | | | | | | | Asian | 17 | 14 | 15 | 16 | 25 | 14 | 1 | 102 | Black | 18 | 24 | 29 | 20 | 17 | 15 | 2 | 125 | Puerto Rican | 17 | 20 | 22 | 24 | 21 | 7 | 0 | 111 | White | 40 | 61 | 36 | 41 | 33 | 22 | 13 | 246 | Total | 198 | 269 | 211 | 248 | 224 | 132 | 42 | 1324 |

The above tables are the number of subjects in each sex, ethnic and age group and to determine how representative the sample was, the body mass index of subjects was compared. The subjects in the study tended to have a lower mean BMI but in both populations, the relation between age and BMI was similar. There was a low BMI in the youngest groups, relatively high BMI in middle-aged people and a progressively lower BMI in older age groups. Most investigations believe body fat increases from young adulthood to middle age and the relation between age and body fat in older individuals is less clear.

References
What is linear regression. (n.d.). Retrieved from http://www.investorwords.com/2829/linear_regression.html
Mott, J. W., Wang, J., Thornton, J. C., Allison, D. B., Heymsfield, S. B., & Pierson Jr, R. N. (1999). Relation between body fat and age in 4 ethnic groups. Retrieved from http://ajcn.nutrition.org/content/69/5/1007.full