# Table 4 Logistic regression analysis

Logistic regression analysis, dependent variable: airway obstruction (n = 1287)
95% Confidence interval
Predictor Regression coefficient Standard error Lower limit Upper limit
Area/Volume phase 3 (g/mol) 31.805 3.290 25.3566 38.2534
log (s3/s2) 6.665 0.843 5.01272 8.31728
log(s3) −4.092 0.542 −5.15432 −3.02968
Volume phase 2 (mL) −0.019 0.003 −0.02488 −0.01312
Constant 2.328 0.795 0.7698 3.8862
1. The table shows the results of logistic regression analysis for the identification of relevant capnovolumetric parameters regarding the presence of airway obstruction. Only the four most relevant parameters were accepted; further parameters did not improve the result in a relevant manner. For the explanation of parameters see Fig. 1. The ratio of slopes of phases 3 and 2 (s3/s2) and the slope of phase 3 were logarithmically transformed prior to analysis in order to approximate normal distributions, and values of 0.03 and 0.05, respectively, were added before taking the logarithm in order to account for zero values. The predicted probability (P) of airway obstruction for each individual patient can be calculated as usual from the equation:
2. $$P=\frac{{\mathrm{e}}^{\mathrm{L}}}{1+{\mathrm{e}}^{\mathrm{L}}}$$
3. in which L = constant + 31.805 * Area/Volume phase 3 + 6.665 * logs3s2 + (− 4.092) * logs3 + (− 0.019) * Volume phase 2. These predicted scores were used in the ROC analysis shown in Fig. 3 