Analytical studies of real systems

For biological systems, the desired experimental studies can be performed. These can be strengthened by investigating physico-chemical system, which can serve as a model. However, this is not possible with socio-political and socio-economic systems where similar types of experiments cannot be designed. In the case of social sciences, one has to depend on the following sequence of activities. 

Sometimes, it may be available or one has to plan for obtaining necessary data [4]. It is sometimes necessary to have cross-sectional data on individual units at a point of time (e.g. data on consumer s income and expenditure on food for a set of families). Another type of cross-sectional data which is often required is related to cross-section of states or of regions. Furthermore, time-series data related to observation over a period of time are also needed. 

These are needed to characterize temporal and spatio-temporal behaviours of the system. For this, it is desirable to distinguish between dependent and independent variables. Furthermore, target variables which play a key role have to identified along with non-target variables which play a secondary role [5]. To illustrate the point, let us examine the dependence of quantity 2, demanded of particular commodity Z which would depend on P, price of commodity Z, Pq price of other commodities, Y income of the consumer and T the suitable measure of the taste. If we take a broader view, 02 would also depend on the following If 

It has to be noted that all the variables are not important. In social and economics sciences, many of such variables are called random variables and expressed as U. Taking a simple example. 

Correlation may be defined as the degree of relationship existing between two or more variables. Correlation may be linear or non-linear. 

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For the analytical study of real systems, it is first of all necessary to identify causes and effects. In the case of electro-osmosis in Chapter 4, we have seen that the number of causes and effects are more than two. In this context, it is therefore desirable to take note of the following ... 

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