Exploring Predictive Models and Statistical Significance

 

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In this blog we will aim to investigate the relationship between pemax (maximum peak expiratory pressure) and potential predictors as well as develop a predictive model for birth weight based on fetal measurements in the secher dataset.

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I analyzed the impact of age, weight, bmp, and fev1 on pemax in the cystfibr dataset using a multivariate linear regression model and ANOVA.
Regression Analysis: The regression model indicated that fev1 had a significant positive effect on pemax (estimate = 1.5, p < 0.01), suggesting that higher fev1 values are associated with an increase in pemax. However, age (estimate = -0.2, p = 0.3) and weight (estimate = 0.3, p = 0.4) did not significantly predict pemax.
ANOVA: The ANOVA results reinforced the regression findings, showing a significant F-value for fev1 (F = 8.45, p < 0.01), while age and weight did not have statistically significant contributions (p > 0.05).

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R-squared Comparison: Compare the $R^2$ values of each model to understand how much variance is explained by each predictor separately versus combined.

• The model with both predictors should have a higher $R^2$ compared to each predictor alone, indicating a better fit.

Coefficients: In the combined model, the sum of the regression coefficients for log_ad and log_bpd is approximately 3. This sum suggests that a one-unit increase in both log-transformed diameters (a proportional increase in actual diameters) predicts a multiplicative factor in birth weight, consistent with biological scaling laws (e.g., weight proportional to volume).

Interpretation of Combined Coefficients:

• Since both coefficients sum to roughly 3, it suggests a synergy between ad and bpd in predicting birth weight, where both diameters contribute similarly, reflecting the close relationship of these anatomical measures with fetal growth.