Matlab 9.10 r2021a

Statistical analyses were performed using MATLAB 9.10 R2021a (MathWorks, Natick, MA, USA). The study utilized a multiple regression model to correlate between estimated BMD values and reference values obtained through dual-energy X-ray absorptiometry (DXA). The features used in the models were denoted as xij, where i represents the feature number and j represents the sample (case) number. The values of xij were normalized using the sample mean and standard deviation, denoted as xi and σi, respectively. Similarly, the reference BMD values, denoted as yj, were normalized using the sample mean and standard deviation, denoted as y and σ, respectively.
To predict BMD estimates, the LR model relied on a weighted combination of 45 features along with a single bias term, represented as yj = w0 + twixij. The weights, wi, were obtained by optimizing the model to reduce the difference between the predicted BMD estimates and the actual BMD values in the dataset, e = jyj − yj2. The study did not employ regularization techniques and did not separate the dataset into training and test subsets.

Statistical analyses were performed using MATLAB 9.10 R2021a (MathWorks, Natick, Massachusetts, USA). The paired t-test was used to verify differences in clinical results and patient demographics between the two groups. Power analysis revealed an effect size of 0.5, the statistical significance of 0.05, and the statistical power of 0.90 for both groups. Mean absolute error was used to compare p-values between the two groups.