Regression analysis polynomial

A eomputer program, PROG2, was developed to fit the data by least squares of a polynomial regression analysis. The data of temperature (independent variable) versus heat eapaeity (dependent variable) were inputted in the program for an equation to an nth degree... 

Tremblay G, Legendre P, Doyon J-F, Verdon R, Schetagne R. 1998. The use of polynomial regression analysis with indicator variables for interpretation of mercury in fish data. Biogeochemistry 40 189-201. 

Fig. 4. Flow scheme of model testing in polynomial regression analysis. Reprinted with permission from Anal. Chem. 55, 153-155 (1982). Copyright ACS.

Finally, it is obvious that the presented polynomial regression analysis with model testing requires a reasonable computational facility. A computer program, RAMP, is available in FORTRAN IV or HPL-BASIC (Jonckheere et al., 1982). 

The model parameters are determined in the following manner the functional relations =/( — 8) and Rincorporated into B.C. of Equation (5.21), are obtained by the polynomial regression analysis of the electrode potential curves and the Kceii versus E curves determined from the Jin, versus AE plots, respectively. It should be borne in mind that (1 — 8) does not represent the average lithium content in the electrode, but the lithium content at the surface of the electrode. In other words, the electrode potential (t) in Equation (5.21) is the potential at the electrode surface. As the relationship —/(I — 8) includes information about the phase transition, we can consider the effect of phase transition on the theoretical CT with the functional relationship =fil — 8), without taking any of the intercalation isotherm. 

Figure 5. Linear, exponential and polynomial regression analysis for magnitude of complex impedance within one evaluation window of frequency sweep from 30 to 100 kHz. 

Polynomial regression analysis proceeds in a manner similar to linear regression (Carnahan et al, 1969). As an example, we shall analyze the second-order polynomial regression the regression for the second-order polynomial is... 

Alternatively, a polynomial regression analysis of the data in Table 11.7 produces the following expression... 

Polynomial regression analysis of the Nd concentration in the melt (y, at%) vs the Nd content in the equilibrium... 

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