Higher order regression functions result better fit for the calibration curve.

Regression analysis is used to predict the dependent variables individually concerning the explanatory available variables and find out the “best fit” line or curve through a series of data in a graph. It is also minimizing the sum of the squares deviations of any experimental data points from the theoretical curve. An important aspect of this analysis is to ensure that the x values are as accurate as possible so that the equation of the regression analysis is valid. Polynomial regression equation allows data to be fitted in general case to any equation where the y values can be described as a function of the x values. Polynomial regression includes quadratic regression (using polynomial 2nd order), cubic regression (using polynomial 3rd order), and higher polynomial regression functions (4th, 5th, and 6th orders) such as logarithmic, exponential, and power regressions. When many points of data do not quite lie on one line, one of the proper polynomial regressions, for instance, exponential or quadratic curves can be used passing through all points approximately for the best fit rather than linear regression. The authors, Sparks et al. studied and obtained contact pressure in the hip joint using paper based Fuji Film sensors and reported the calibration curve for the contact pressures as a function of stain intensity in Figure A.1, Appendix A. As seen, the calibration curve of their contact pressures are fitted using the quadratic regression equation. However, the 2nd order curve used in their study is not suitable to represent their calculated parameters for an appropriate fit especially for the higher x values, for example, y 1⁄4 1.875 MPa for x 1⁄4 200, considering the equation in Figure A.1. But, y value can be seen about 3 MPa for x 1⁄4 200 as seen in the graph. It is necessary to select a suitable regression equation to represent the best fit of the data. Based on the ideas given in Ref., using a 5th order curve is an appropriate approach for the best fit of the Fuji-film calibration data characteristics. In addition, the 5th order regression equation used by Muriuki et al. in their studies that shows the best fit. Therefore, the authors are suggested to use higher order regression equation to represent more precise fit of their calibration data.