# 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 