are age weight and height related to body fat percentage

Siri 1956suggested that the body consists of two components - lean tissue andadipose tissue and that the percentage of body fat can be calculatedusing the formula:B = 1/D*[ab/a-b] - [b/a

PROJECT REPORT Subject: MAS202 Teacher: Phạm Thanh Hiếu

Group: 2

-Are age, weight, and height related to body fat percentage?

Group member Nguyễn Xuân Tùng - HS160884

Đặng Văn Bảo Linh - HS160591

Nguyễn Ngọc Lan - HS160578

Trần Việt Dũng - HS160773

An Văn Hải - HS160618

Table Content The presentation consists of 7 parts from sheet 3 to sheet 9

Sheet 1: Report Showcase data and summarize results

Sheet 2:

Data&Descriptive measures Original data and descriptive statistics

Sheet 3:

Boxplots&Histograms

Boxplots và histograms

Sheet 4: 95% CI 95% confidence interval for population

mean

Sheet 5: Test claim Hypothetical test for population mean

Sheet 6: Multiple

Sheet 7: Output analysis Analysis of multivariate linear regression

results

The first part is an introduction to the topic and figures:

- What is body fat and how is it calculated: Many health experts suggest that people use body fat percentages to assess their health Siri (1956) suggested that the body consists of two components - lean tissue and adipose tissue and that the percentage of body fat can be calculated using the formula:

B = (1/D)*[ab/(a-b)] - [b/(a-b)]

- Research shows that people with a high percentage of body fat are more likely to develop cardiovascular disease and metabolic syndrome, but if the percentage of body fat is too low, it is not necessarily good The American Journal of Clinical Nutrition puts healthy body fat rates based on age (same as in the table) Women generally have a higher percentage of body fat than men And body fat will naturally increase

as we age

- Brief data description: Data on the fat ratio of 251 men, their age, height and weight with the unit: Body fat percentage (%), Age (years), Weight (lbs, 1 lbs = 0.45359237 kg), Height (inches, 1 inch = 2.54 cm)

- Purpose: Conduct confidence intervals, test assumptions for population mean and linear regression to answer 2 questions:

+ Is there evidence that the average population in terms of body fat percentage will be greater than 20%?

+ Is there any evidence that men's age, weight, and height are related to their body fat percentage?

- Conclude: The regression model showed that 51.62% of the variation

in body fat ratio was explained by variations in age, weight, and height

- The hypothetical test results for the angular coefficient show that all three independent variables (age, weight, height) are related to the percentage of body fat

- Applied in practice, the regression model can be applied to predict the body fat percentage of 1 man based on age, weight, and height

- From the topic above, we can learn how to have 1 healthy, safe percentage of fat:

1 Caloric Balance:

Maintaining a healthy percentage of body fat requires the number of calories consumed to be equal to the number of calories burned

1 Nutritious:

The diet should include high-quality protein that accounts for 10-15% of daily calories, 20-30% should come from heart-healthy fats, the remaining 55-60% should come from carbohydrate-rich foods such as whole grains, fruits and vegetables

2 Physical training:

To keep the percentage of body fat at a healthy level it is necessary to balance it with lean muscle tissue The optimal way to build and maintain muscle tissue is physical training

3 Aerobic exercise:

Aerobic exercise can also help increase the amount of calories burned each day In addition, this type of exercise — especially high-intensity exercises

— improves heart and lung health and can reduce the percentage of visceral fat, an unhealthy fat that surrounds internal organs that has been linked to heart disease and type 2 diabetes

[Data&Descriptivemeasures]

This is the original data we have and the statistical data tables describe

From the Percentage of fat table, the mean is 19,0378 The median is equal

to 19.2% The standard deviation is 8.1908 and the variance is 67,0884 The range is 40.1; min and max are 0 and 40.1

From the Age table, the mean is 44.8606 The median is equal to 43 The standard deviation is 12.6213 and the variance is 159.2965 The range is 59; min and max are 22 and 81

From the Weight table, the mean is 178.7647 lbs The median equals 176.25 The standard deviation is 29.3382 and the variance is 860.7278 The range is 244.65; min and max are 118.5 and 363.15 lbs

From the Height table, the mean is 70.1733 inches The median equals to 70 The standard deviation is 3.6494 and the variance is 13.3183.The range is 48.25; min and max are 29.5 and 77.75 inches

It can be seen from the box and whisker plot that the body fat percentage has Q1=12.4, Q2=19.2 and Q3=25.3 Most men have a body fat percentage between 10 and 30% Only 1 person exceeded 40%

It can be seen from the box and whisker plot that the weights have

Q1=158.25, Q2=176.25; and Q3=197 lbs Most weigh between 138.5 and 218.5 lbs Very few people weigh over 250 lbs

It can be seen from the box and whisker plot that the ages have Q1=35, Q2=43, and Q3=54 Most of those surveyed are young and middle-aged men

It can be seen from the box and whisker plot that height has Q1= 68.25, Q2=

70, and Q3=72.25 inches All men in the data, with the exception of one, are 59.5 inches or more tall

95% Confidence Interval for population mean: Body Fat

With 95% confidence, the population mean for body fat percentage would be in the range 18.0196 to 20.056

95% Confidence Interval for population mean: Age

With 95% confidence, the population mean of age would be between 43.2916 and 46.4296

95% Confidence Interval for population mean: Height

With 95% confidence, the population mean of height would be between 69.7196 and 70,627 inches

95% Confidence Interval for population mean: Weight

With 95% confidence, the population mean of weight would

be between 175,1176 and 182.4118 lbs

- The mean age is 44,8686 According to the American Journal of Clinical Nutrition, a healthy body fat percentage for men aged 40 to 59 should decrease by about 11% to 21% So the question is at 0.05 level

of significance, is there evidence that the population mean of body fat will be greater than 20% ?

H0: μ=20 (%)

H1: μ>20 (%)

t_stat = (sample mean-population mean)/standard error = -1,861

degree of freedom = n-1= 251-1 = 250 => t_critical value = t_0.05; 250 Since -1.861 < 1.6510, do not reject H0

We can conclude: There is insufficient evidence that the population mean of body fat will be greater than 20%

Here are the results of the regression run

After running the regression in excel, we see:

- R square = 0.5162 means that 51.62% of variation in body fat percentage is explained by variation in age, weight and height

- The number of observations was 251 men

- Significance F or p-value < level of significance 0.01 so the regression model is statistically significant

Question: Is there any evidence that men's age, weight, and height are related to their body fat percentage?

- Looking at the coefficients column, the meaning of the slopes and the coefficients of freedom can be explained as follows:

- When all independent variables were zero, mean body fat percentage was predicted to be 15.7027

+ For every 1 year increase in age, average body fat percentage is predicted to increase by 0.1692

+ For every 1 lbs increase in weight, average body fat percentage

is estimated to increase by 0.1936

+ For each 1 inch increase in height, the average body fat percentage is estimated to decrease by 0.5538

- The linear regression model is:

y = 15.7027 + 0.1692 x1 + 0.1936 x2 - 0.5538 x3

+ y is the estimated percentage of body fat

+ x1: age (years)

+ x2: weight (lbs)

+ x3: height (inches)

- Based on this model, we can estimate the body fat percentage of a 20 year old male, weighing 150 lbs (~68kg), 70 inches tall (~178cm) as 9,3607% =(15.7027 + 0.1692) * 20 + 0 , 1936 * 150 - 0.5538 * 70

- Test assumptions for slope

- We will compare the results p-value and level of significance 0.01 to conclude

- p_value of age < 0.01 Therefore, this coefficient is statistically significant and age is related to body fat percentage

- p_value of weight < 0.01 Therefore, this coefficient is statistically significant and weight is related to body fat percentage

- p_value of height < 0.01 Therefore, this coefficient is statistically significant and height is related to body fat percentage

https://www.kaggle.com/datasets/fedesoriano/body-fat-prediction-dataset