Analyzing the Impact of Various Criteria on Blood Pressure Through General Linear Model by Box-Cox Transformations

Blood pressure is a key indicator of cardiovascular health, reflecting the force exerted by blood against arterial walls. Data transformation tools are essential in statistical analysis for improving assumptions necessary for linear models, such as normality, linearity, and homoscedasticity, especially when these assumptions are violated. These techniques are especially helpful for correcting distortions in data structure and enhancing the validity of General Linear Models (GLMs).    In this study, we applied the Box-Cox transformation, a method from the family of power transformations, to improve a linear regression model. Our objective was to identify the most appropriate power transformation to enhance model performance and interpretability, using statistical criteria on blood test datasets collected from Azadi Hospital in Duhok. These evaluation criteria are essential for the accurate interpretation of data, as they assess the modeBlood pressure is a key indicator of cardiovascular health, reflecting the force exerted by blood against arterial walls. Data transformation tools are essential in statistical analysis for improving assumptions necessary for linear models, such as normality, linearity, and homoscedasticity, especially when these assumptions are violated. These techniques are especially helpful for correcting distortions in data structure and enhancing the validity of General Linear Models (GLMs).    In this study, we applied the Box-Cox transformation, a method from the family of power transformations, to improve a linear regression model. Our objective was to identify the most appropriate power transformation to enhance model performance and interpretability, using statistical criteria on blood test datasets collected from Azadi Hospital in Duhok. These evaluation criteria are essential for the accurate interpretation of data, as they assess the model’s quality and reliability. The criteria used included: adjusted R-squared, Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), F-statistic, Maximum Likelihood Estimation (MLE), Root Mean Square Error (RMSE), and the Shapiro–Wilk test. These measures also guided the selection of the most appropriate GLM. We can conclude that different  values optimize different model performance aspects:  balances good model fit (  F-statistic).  gives the most accurate predictions (lowest error).  improves likelihood and residual normality. A computational algorithm was proposed to estimate the optimal power parameter, and the results of the criteria were discussed and compared. Based on the adjusted R-squared criterion, an optimal λ value was identified, indicating a strong model fit.l’s quality and reliability. The criteria used included: adjusted R-squared, Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), F-statistic, Maximum Likelihood Estimation (MLE), Root Mean Square Error (RMSE), and the Shapiro–Wilk test. These measures also guided the selection of the most appropriate GLM. We can conclude that different  values optimize different model performance aspects:  balances good model fit (  F-statistic).  gives the most accurate predictions (lowest error).  improves likelihood and residual normality. A computational algorithm was proposed to estimate the optimal power parameter, and the results of the criteria were discussed and compared. Based on the adjusted R-squared criterion, an optimal λ value was identified, indicating a strong model fit.