Appendix. Linear Least-Squares Analysis

A major problem in interpreting data is to determine whether experimental quantities are correlated on the basis of an assumed theoretical model. Since there are always errors of measurement, correlation is never exact and a method forjudging whether correlation is significant is required. From probability theory random errors have a Gaussian distribution. 

If all errors are random, the best procedure for fitting data to a model is the method of least squares. 

As an example, consider the data presented in Fig. 4.6 experimental values of the decay constant x are plotted against experimental values of the quantity [M] + [L] + IjKi. If there are N data with ordinates yi and abscissas Xi the problem is to test whether the functional form 

Chemical Thermodynamics, 3rd ed. (San Francisco Freeman, 1974), Chapter 3. 

For an introduction to data analysis see H. D. Young, Statistical Treatment of Experimental Data (New York McGraw-Hill, 1962), in particular, pp. 101-132. A comprehensive treatment is given by N. R. Draper and H. Smith, Applied Regression Analysis (New York John Wiley, 1966), Chapter 10. 

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Many sources of error complicate the deduction of a rate law from kinetic data. In each experiment the time dependence of the concentration has a specific functional form which is usually not self-evident from the data unless isolation or relaxation methods are used. In addition no data ever precisely fit a trial function. However, if all errors in the experiment are random, probabilistic methods can be used to determine whether the trial function is reasonable and to estimate the parameters of the function. As long as only a single chemical process is significant, isolation and relaxation data are most readily treated using linear least-squares analysis, described in the Appendix. This procedure provides the most reliable estimate of the decay constant. Then, by varying experimental conditions the concentration dependence of the decay constant can be obtained. With such information probabilistic methods are again useful. A presumed rate... 

Fig. 6. 15 A suite of five whole-rock samples of the Wyatt Formation collected by V.H. Minshew from outcrops between Mt. Wyatt and Mt. Gardiner in the Scott Glacier area define two straight lines labeled A and B derived by least-squares linear regression. Line A which includes all five samples plus one duplicate analysis yields a date of 524 13 Ma and a high initial Sr/ Sr ratio of 0.711919 0.000547 (la). Line B is defined by three selected samples and corresponds to a precise date of 802 2 Ma but it has an impossibly low initial Sr/ Sr ratio of 0.69775. We conclude that the igneous rocks of the Wyatt Formation are older than 524 13 Ma but younger that 802 2 Ma. These previously unpublished data by G. Faure are presented in Appendix 6.133. In addition. Appendices 6.7.3.1 and 6.7.3.2 contain modal analyses and chemical compositions of rocks of the Wyatt Formation from Minshew (1967)...

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