Blood Characteristics Analysis

Table of Contents

• Data Sourcing
• Data Presentation
• Exploratory Analysis
• Data Analysis
• Insights
• Recommendations

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Data Sourcing

• Background information

The Australian Institute of Family Studies (AIFS) is a Melbourne based Australian Government statutory agency established in 1980 under the Family Law Act 1975.
The Institute has a proud record of high-quality, responsive and impartial research into the wellbeing of (Australian) families. The vision of Institute is to make a positive contribution to the wellbeing of families by advancing understanding of the factors affecting families and communicating findings to policy makers, service providers and the broader community.

• Source of the data Cook, R. D., and Weisberg, S. (1994). An Introduction to Regression Graphics. Wiley, New York.

• Aim of the study: Understand how data on various characteristics of the blood varied with sport body size and sex of the athlete.

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Data Presentation

• The data are collected from 102 male and 100 female athletes.
  They consist of 13 variables.
  
  The first two variables are categorical and especially are the gender of the 2 athlete and their sport.
  The remaining 11 variables are various measurements made on the athletes.
  The dataset is available in the file sport.txt.

• Dataset characteristics
  The Dataset has the following fields:
  Sex: a factor with levels {male, female}
  Sport: a factor with levels {BBall, Field, Gym, Netball, Row, Swim, T400m, TSprnt, WPolo }
  RCC: red blood cell count, in 10^{10} per liter
  WCC: white blood cell count, in 10^{10} per liter
  Hc: hematocrit, percent
  Hg: hemaglobin concentration, in g per decaliter
  Ferr: plasma ferritins, ngr per decaliter
  BMI: Body mass index, 102kg/cm2
  SSF: sum of skin folds
  X.Bfat: percent Body fat
  LBM: lean body mass, kg
  Ht: height, cm
  Wt: weight, kg

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Exploratory Analysis

Exploratory Analysis

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Data Analysis

1. Linear Regression Weight and Height
2. Ferretin Multiple Linear Regression
3. Ferretin Linear Regression with Log Transformed Data
4. Poisson log-linear model for white blood cell count
5. Proportion of white blood cells with Binomial Log Regression
6. Classification for sport and sex

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Insights

• Weight and Height Relationship

The interpretation indicates that Height has a significant effect on Weight, with each additional centimeter of Height increasing Weight by 0.42 kilograms, according to the model.
The model explains a large portion of the variability in Weight, and the predictions are expected to be accurate within approximately 11.05 kilograms, with prediction intervals providing an estimate of the range within which future observations are likely to fall.

• Ferretin as a dependent variable with Linear Regression

The multiple linear regression model for predicting Ferritin levels and it does not seem to be a good model mainly due to violation of the linear regression assumptions, so we will try to use the logarith transformed data in order to improve the model and address any violations of the assumptions.

• Log(Ferretin) as a dependent variable with Linear Regression

The log-transformed model has shown improvement in terms of diagnostics, although the normality assumption may still not be fully addressed.
So the model we prefer is the log model.

• White blood cell count (WCC) as a dependent variable with Poisson log-linear model

The Poisson model fits well the data. As the model is not overdispersed.
Using the final model, we can make predictions for specific scenarios for the white cells of each person.

• Fitting a binomial logistic regression model to predict the proportion of white blood cells

The factors that are associated with changes in the proportion of white blood cells are X.Bfat and Ht, it suggests that higher body fat levels are associated with an increase in the proportion of white blood cells.

Using the final model, we can make predictions for specific scenarios, such as predicting the expected amount of white blood cells for a female athlete involved in Gym activities.

• Classification

The high accuracy rates of the k-nn model and the decision tree model for predicting sex suggest that the features used in the analysis (e.g., LBM, X.Bfat) are informative for distinguishing between male and female athletes. These features may be important indicators of gender differences in athletic characteristics. The LDA model achieved a correct classification rate of 63.8% for predicting sports based on the provided features. While the performance is moderate, it suggests that the model can capture some patterns in the data.

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Recommendations

• Consider evaluating additional factors that may influence weight, such as gender, or body composition, for a more comprehensive model.

• Consider whether additional non-linear transformations or alternative functional forms for predictors could better capture the relationship with Ferritin levels. Polynomial terms or other non-linear transformations may help address non-normality and improve model fit.

• Finally explore opportunities for further investigation, model refinement to improve predictive performance and robustness.