NHANES Analysis Summary

This README provides a structured summary of findings, model diagnostics, and recommendations based on the NHANES dataset analysis.

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1. Key Regression Model Results

BMI Model (Ordinary Least Squares - OLS)

• Variables Used: height, weight
• R-squared: ~1.0 (indicates a perfect fit, likely due to multicollinearity)

Coefficients:

• height: -0.3013 (significant, p = 0.000)
• weight: 0.3561 (significant, p = 0.000)

Issues Identified:

• Multicollinearity: High condition number (> 4900). Strong correlation between height and weight.
• Heteroscedasticity:
  • Breusch-Pagan test p ≈ 0 (rejects homoscedasticity).
  • Residual plots show non-constant variance.

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Weighted Least Squares (WLS) Model

• Transformation: log(bmi) ~ log(height) + log(weight)
• R-squared: ~0.999

Diagnostics:

• Heteroscedasticity still present (Breusch-Pagan p ≈ 7.6e-23)
• Transformation improves linearity but doesn’t fully resolve variance issues.

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Blood Pressure Model (Logistic Regression)

• Variables Used: bpsystol, bpdiast
• Outcome: High blood pressure (HBP)
• Results: Both variables significantly associated with HBP.

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2. Model Diagnostics

Assumptions Check

• Normality:
  • QQ plots show deviation (e.g., residual skewness = 0.684)
• Linearity:
  • Log transformations improved model form
• Homoscedasticity:
  • Breusch-Pagan consistently rejects equal variance
  • Recommendation: Use robust standard errors or alternative models (e.g., GLS)
• Independence:
  • Durbin-Watson ≈ 2 (suggests no autocorrelation)

Influential Observations

• Cook’s Distance: Most points within acceptable range
• Leverage: No high-leverage points found (3*(k+1)/n threshold)

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3. Data Cleaning & Preprocessing

• Missing Values:

  • High: lead, tgresult, fhtatk (~50%) → consider imputation or exclusion
  • Low: hlthstat, heartatk, diabetes (~0.02%)

• Categorical Variables:

  • Encoded sex, race, psu
  • Check for typos (e.g., orace vs. race)

• Outlier Handling:

  • Filtered using 10th–90th percentile
  • Confirm data retention after filtering

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4. Recommendations

Addressing Multicollinearity

• Option 1: Drop a predictor (e.g., weight)
• Option 2: Apply ridge regression

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Fixing Heteroscedasticity

• Use Robust Standard Errors:

bmi_model_robust = sm.OLS.from_formula('bmi ~ height + weight', data=nhanes).fit(cov_type='HC3')

• Try Other Transformations: e.g., sqrt(bmi), 1/bmi

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Predictive Modeling for Diabetes

• Logistic Regression:

diabetes_model = smf.logit('diabetes ~ age + bmi + sex + race', data=nhanes).fit()

• Feature Importance: Evaluate coefficients or use permutation importance

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Descriptive Analysis

print(nhanes[['weight', 'height', 'age']].mean())
sns.histplot(nhanes['region'], discrete=True, shrink=0.8)

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Code Improvements

• Fix Typos: e.g., depnedant variabels → dependent variables
• Verify Column Names: (e.g., hct vs. HCT)
• Weight Calculation:

waight = 1 / (bmi_model.resid**2 + 1e-6)  # Prevent division by zero

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5. Next Steps

1. Complete Data Cleaning: Handle missing and inconsistent values
2. Re-run Models: With robust estimators or transformed variables
3. Generate Visuals: Residual plots, histograms, correlation heatmaps
4. Report Results: Emphasize strong predictors and relationships

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