Types of correlation, Applied Statistics

Type of Correlation

1.      Positive and Negative Correlation:

2.      Simple Partial and Multiple Correlations.

3.      Linear and  Non linear or Correlations:

1. Positive and Negatives Correlations: If changes in two variables are in same direction. Increase in one variable is associated with the corresponding increase in other variable, the correlations is said to be positive. For example increase in price and increase  in supply, increase in father ages and increase  in sons ages, higher amount  of capital employed  associated with higher expected profit etc.

On the other hand if variations or fluctuations in two variables are in opposite direction or  in other  words the  increase in one  variable is associated with the corresponding   decreases  in other  or vice  versa  the correlation is said to be negative . For example, increase in price associated with the decrease in demand and vice versa .Thus price and demand have negative correlation. 

2. Linear and non linear Correlation: The distinction between linear and non linear correlation is based upon the constancy of the ratio of change between the two variables. If    the amount of changes in one variable tends to bear constant ratio of change in the other a variable, the correlation is said to be linear. For example, if in a factory raw material or numbers of direct workers are doubled, the production is also doubled, and vice versa correlation would be linear.

On the other hand correlation would be called curvilinear if the amount of change in one variable does not bear a constant ratio of change in the other variable. For example the amount spent on advertisement will not bring the change in the amount of sales in same ratio. It means the variations in both the variables are not inconstant ratio.

Thus linear and non linear correlation may also be positive or negative .It is clear from the following chart.

Thus it is clear from the above that:

1.      If changes in two variables are in the same direction and in constant ratio. The correlation s is linear positive. For example every10% increase in inflation results in 15% increase in general price level. Correlation   between inflation and general price level would be linear and positive.

2.      If changes in two variables are in the opposite direction in constant ratio, the correlation is linear negative. For example every 5% increase in price of a commodity is associated with 10% decrease in demand, the correlation between price and Demand would be negative linear.

3.       If changes in two variable are in the same direction but not inconstant ratio, the correlation is positive nonlinear. For example every increase  of 10%  quantity of money  in circulation, the general price level increases by 5or6%  the   correlation  between  inflation  and general price level would  be positive  curvi  linear.

4.      If changes is two variables are in opposite direction and not inconstant ratio, the correlation is negative curvilinear. For example for every  5%  increase in price  of a commodity is associated with 2%  to 10%  decrease in demand, the correlation between  price and demand is said to be negative and curivilinear  

3. Simple, Partial and Multiple Correlations: The distinction between simple, partial and multiple correlations   based   upon the number of variables studied. When only two variables are studied, it is as case    of simple correlation. On the other hand when three or more variable are studied, it is a problem of either multiple or partial correlation.

When three or more variable are studied simultaneously, it is called multiple correlation. When a study of yield per acre of wheat is studied with a unit change in fertilizers and the rainfall,it is a problem of multiple correlation, whereas  in partial correlation more than two  variables are studied, but consider the influence of a third variable on the two variables influencing variables being kept constant, it is a problems  of partial correlation. For example, if the change in yield of wheat and rice is studied with reference to a unit of fertiliser or rainfall, it is a case of partial correlation. 

Posted Date: 9/27/2012 6:21:07 AM | Location : United States







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