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12 11 10 9 8 7 Y-axis (mm) 12 11 10 9 8 7 P0 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 6 5 4 Y1 3 2 1 Y10 Y2 Y3 Y4 Y5 Measured distance (mm) Y9 Y8 Y7 Y6 Y5 6 5 4 Y6 Y7 3 2 1 Y8 Y9 X-axis (mm) 1 2 3 4 5 6 7 8 9 10 11 12 Y10 Y = Î²Ì0 + Î²Ì1 X Y4 Y3 Y2 Y1 Reference distance (mm) 1 2 3 4 5 6 7 8 9 10 11 12 (a) 10 repeated COP measurements at each point P were obtained, averaged and the relative position, Y , with respect to the point P0 was computed. In total, for each of the points, four average values (distances) were computed, two in the P0 â P10 direction and two in the P10 â P0 one. (b) The averaged measured values of the force platform system (Y ) are plotted against the quantity values (X ) that have been taken by the millimetric grid. Then, a linear regression analysis has been used to maintain the calibrated system in a state of statistical control. Figure B.5 The static performance characteristics of the force measurement system was studied by plotting the output signal (Y ) obtained by the force platform (Fig. B.5a) system against the known input signal (X ) in order to generate a scatter plot, wherein a straight-line was fitted with the method of least squares, as it is assumed that the output signal is linearly proportional to the input signal (Fig. B.5b). It is assumed that biases are corrected by the manufactureâs calibration procedure, therefore, only the uncertainties of the correction are presented. In order to estimate the intercept and the slope of the fitted line, the method of least square error is used which minimizes the sum of the squared residuals by taking into consideration that nominal values have no uncertainties and the uncertainty in the measured values is constant over the range of the curve fit. Once the coefficients of the linear model are found, the estimated regression lines for the measured signals can be read. The residuals of the fitted model (Fig. B.6) were analyzed to test the goodness of the fitted linear regression models and to identify possible outliers using the getOutliers() function of the package extremevalues (Loo, 2010) in R environment (R Core Team, 2013). B.3.4. Error Model and Sources The error model for "COP is the sum of the errors encountered during the measurement process "COP = "res + "ran + "reg + "lnr + "hys where "res is the error associated with the digital resolution of the system display "ran is the error associated with repeated measurements 151