In this project, I use linear regression to explore the relationship between BMI, age, and the average number of positive risk factors for metabolic syndrome. By analyzing the slopes and R2 values from the regression models, I will determine how strongly BMI and age (Age vs. BMI) influence the number of risk factors.
Linear regression models the relationship between a dependent variable (y) and independent variables (x) using a linear equation. The interpretation of the slopes (β) from the linear regression models provides valuable insight into how much the average number of risk factors changes with a one-unit increase in either BMI or age. A positive slope indicates that an increase in the independent variable, whether BMI or age, is associated with an increase in the number of risk factors, while a negative slope would suggest a decrease.
The coefficient of determination, R², measures the proportion of variance in the dependent variable explained by the independent variables. This metric offers an indicator of how well the independent variable (BMI or age) predicts the number of risk factors. The interpretation of R² values ranges as follows: a low R² (0-0.3) indicates a weak relationship where BMI or age explains little of the variability in the number of risk factors; a moderate R² (0.3-0.6) suggests a fair amount of the variability is explained; a high R² (0.6-0.9) represents a strong relationship where most of the variability is explained; and a very high R² (0.9-1.0) indicates an extremely strong relationship, with BMI or age almost entirely predicting the number of risk factors.
By analyzing the slopes and R² values from the regression models, I will assess how strongly BMI and age influence the average number of positive risk factors for metabolic syndrome. The results of this analysis will help determine which factor, BMI or age, has a more significant impact on the risk profile and may provide insights into targeted interventions for reducing the prevalence of metabolic syndrome.
The slope and R² are both important metrics in linear regression analysis, but they provide different insights and serve distinct purposes. The slope represents the rate of change in the dependent variable, which in this case is the average number of positive risk factors for metabolic syndrome. It tells us how much the dependent variable is expected to increase or decrease when the independent variable increases by one unit. A positive slope indicates that as the independent variable increases, the dependent variable also increases, while a negative slope suggests a decrease in the dependent variable as the independent variable increases. The slope thus offers direct insight into the nature and magnitude of the relationship between the variables.
In contrast, R², the coefficient of determination, measures the proportion of variance in the dependent variable that is explained by the independent variable(s) in the model. It provides an overall indication of how well the independent variable(s) account for the variability in the dependent variable. Unlike the slope, R² does not give information about the direction or magnitude of the relationship but rather assesses the strength and explanatory power of the model as a whole.
The key difference lies in the type of information each metric provides: the slope focuses on the magnitude of the relationship, showing how changes in the independent variable affect the dependent variable, while R² evaluates the strength of the model, indicating how well the independent variable(s) predict the dependent variable. In summary, while the slope gives a detailed understanding of the relationship between specific variables, R² offers a broader assessment of how well the model captures the overall variability in the data. Both metrics are essential for interpreting the results of a regression analysis but serve different interpretative purposes.
The dataset used in this analysis, 'df_adult_updated.csv,' is a novel synthetic representation of the US adult population, designed to reflect realistic distributions of age and BMI. It includes metabolic health metrics that simulate real-world data. It achieves a calculated 34.58% prevalence of metabolic syndrome, closely matching national estimates. Full analysis of this dataset can be found at: https://github.com/Compcode1/synthetic-metabolic-dataset
The coding approach in this project utilizes PostgreSQL for database management, where we created and managed tables to store and analyze the data. We used Python with the psycopg2 library to interface with the PostgreSQL database, allowing us to execute SQL commands directly from Python scripts. The analysis involves creating tables, inserting data, and running complex queries to calculate average risk factors by BMI and age.
We also implemented user management within the PostgreSQL environment by creating roles with different levels of access. Specifically, we created a read-only user who can view data without making changes and a read-write user who has permissions to both view and modify data. This approach ensures data security and integrity while allowing different types of access based on user roles.
The analysis offers significant insights into how BMI and age relate to the average number of positive risk factors for metabolic syndrome. The slope for BMI is 0.074, indicating that for each unit increase in BMI, the average number of risk factors rises by approximately 0.074. This suggests that BMI has a relatively strong impact on the number of risk factors, particularly in the short term. Conversely, the slope for age is 0.021, suggesting a smaller increase in risk factors with each additional year of age. Although both BMI and age are influential, BMI appears to have a more immediate effect on the risk factors.
It is important to note that the R2 value for age is 0.858, higher than the 0.728 for BMI. This indicates that age explains a greater portion of the variance in the average number of risk factors, suggesting a stronger overall relationship between age and these risk factors. This higher R2 value implies that age, despite having a smaller slope, is a more consistent predictor across its wider range, explaining more of the variability in risk factors than BMI does.
It's also crucial to consider the differing scales of age and BMI. Age spans a much broader range than BMI, which could influence the analysis by naturally providing more variability. The broader range of age might contribute to the higher R2, while the narrower range of BMI could result in a steeper slope. This issue is explored in this project.
In practical terms, this analysis highlights the importance of both managing BMI for its immediate impact on health and considering age as a critical factor over the long term. While BMI is a key factor in the short term, the aging process consistently increases the risk of metabolic syndrome over time. Health strategies should therefore address both BMI management and age-related risk.