# Tutorial: How to draw the line in biomedical research

1. Johns Hopkins University School of Medicine, United States
2. Johns Hopkins Bloomberg School of Public Health, United States
3. Howard Hughes Medical Institute, Johns Hopkins University School of Medicine, United States
2 figures

## Figures

Figure 1 Different types of best-fitting straight lines. These graphs show the best-fitting straight lines through the same five data points as calculated by minimizing the sum of the squares of the vertical residuals, which assumes that x is the independent variable (A); horizontal residuals, which assumes that y is the independent variable (B); and perpendicular residuals which involves no assumptions about the variables (C).
Figure 2 Best-fitting straight lines for three data sets reported by Ressler and co-workers (Ressler et al., 2011). For each of these data sets, best-fitting lines have been calculated by minimizing the sum of the squares of vertical residuals (green), horizontal residuals (blue) or perpendicular residuals (red). The variables in each data set are explained in the text; the data are taken from Figures 1a (A), 4a (B) and 4c (C) in Ressler et al. The agreement between the three lines is relatively poor, as expected from the low values of R2, where R is the correlation coefficient. The orthogonal or Deming regression shown by the red lines is not available in Microsoft Excel, but it can be calculated with Excel add-in freeware provided by Jon Peltier (peltiertech.com/WordPress/deming-regression-utility), with the “r” statistics package (www.r-project.org), and with various commercial software packages including Analyse-it (analyse-it.com) and MedCalc (www.medcalc.org/).

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