THE MEAN VALUE CONCEPT IN MONO-LINEAR REGRESSION OF MULTI-VARIABLES IN GEOSCIENCE STUDY

Many isotopic indicators in nature are variables related to more than one source influence. The measured Oxygen isotope ratio delta¹⁸O(M) from coral, the measured ¹⁰Be record from marine,ice core and loess, and the measured magnetic susceptibility formed by the ferromagnetic mineral in loess all are dependent variables y(x₁,x₂) related to two independent sources (independent variables). In geoscience research, the data analysis is concerned with calculating the mono-linear regression of the dependent variable y(x₁,x₂)with either the independent variable x₁ or x₂ respectively. There is an important ignored conceptual problem to be clarified, that is, what is the implication involved in a mono-linear regression of multi-variables?

we clarified "the mean value concept" in a mono-linear regression of multi-variable system. We described in detail the applications of "the mean value concept" to reconstruction of the past 90 -year salinity of the sea water in Xisha islands and to tracing the past 80 ka paleo-geomagnetic events from the Luochuan Loess ¹⁰Be record.

The presented "mean value concept" is that a mono-linear regression of multi-variables, such as y(x₁,x₂) vs x₁, is carried out around the average x₂ .Namely, the estimated value y_e of the regression equation y_e=ax₁+b is the sum of both the varying contribution by x₁ and the constant contribution by x₂ that is, y_e=y(x₁)+y(x₂)=y(x₁)_x.

The reconstructed past 90 years salinity of the sea water in Xi sha Island by using the "mean value concept" "is in good compliance with the data provided by the observation station. Comparing the first 12 year's salinity between the calculated and observed curves, their arithmetic average error, relative error and the maximum relative error are 0.33°ë, 0.97% and 2.67%.

The traced past 80ka paleogeomagnetic intensities reveals important magnetic events, such as Laschamp and Mono-Lake , Though many geologists considered that it is impossible to trace the geomagnetic events from loess ¹⁰Be due to its complexity of deposition, the trace results in this paper have shown that the trace of the paleo-magnetic events form the complex loess ¹⁰Be is not impassable by using the "mean value concept".

The "mean value concept" has clarified the real meaning of a mono-linear regression of multi-variables which is frequently and extensively applied in various research and would be useful in other fields.