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A comprehensive statistical analysis on the relationship between the two variables investment fund performance andinvestment fund management fee.
The project aimsat drawing (statistical) conclusions about the relation(if any) between theperformance of the investment funds(in terms of price) and money spend as thecost of managing the respective funds, the significance of the relation andthereby provide some support in decision making for higher level managementregarding this. Please note that the project only attempts to find if changein one variable is accompanied by the change in the other and this in no wayestablishes the cause and effect relationship i.e. we cannot conclude, atleast by this exercise, whether increase in spending on the management feescauses increase in the fund performance. (the cause and effect relationshipcannot be found by just using statistical techniques but it also requires theexhaustive study of the nature of the funds and the management involved). Ifthe correlation exists between the above two factors then it could mean eitherone of them influences the other or both of them influence each otherconsistently or intermittently or both of them are influenced by some otherthird factor or the correlation could be out of pure chance(i.e. because of thechoice of a wrong sample).
We come acrosssimilar situations in reality where we need to find whether two or moreentities are related to one another and the nature and the degree of theirrelationships. For example the age of husband and wife, price of a commodityand the amount demanded, an increase in rainfall up to a point and productionof rice etc. (examples involving only two entities are considered here becauseit would be easier to discuss, and the given project also involves only twoentities and the same ideas can be extended to the cases involving more thantwo entities). Since the entities assume different values depending upon thetime place or persons these are referred to as variables in Statistics. If arelationship (measurable) exists between the two variables then the variablesare said to be correlated. The measure of the correlation called thecorrelation coefficient or the correlation index gives the degree and thenature of the correlation (i.e. increase in one variable corresponds toincrease or decrease in the other variable) in terms of a number. Thecorrelation analysis deals with the techniques used in measuring the closenessof the relationship between the variables.
We give someimportant definitions in this regard:
Correlation Analysis deals with the association between two or more variables. (By Simpson and Kafka).
If two or more quantities vary in sympathy so that movement in one tends to be accompanied by a corresponding movement in the other(s) then they are said to be correlated.(by L.R.Connor)
When the relationship is of a quantitative nature, the appropriate statistical tool for discovering and measuring the relationship and expressing it in brief formula is known as correlation. (Croxton and Cowden).
There areseveral ways of classifying correlation. Three of the most important are:
positive (direct) or negative (inverse)correlation:- if one variable increases the othervariable also increases on average and if one decreases the other decreases onaverage then they are said to be positively correlated. If one variableincreases and the other decreases on average and if one decreases the otherincreases on average the two are said to be negatively or inversely correlated.
Simple, partial and multiple correlation:- when only two variables are studied it is a problem of simplecorrelation. When three or more variables are studied it is a problem of eitherpartial or multiple correlation. In multiple correlation three or morevariables are studied simultaneously. For example, when we study therelationship between the amount of fee paid to a plastic surgeon, thecomplexity of the operation and the quality of their work (in terms of resultsetc.) then it is a problem of multiple correlation. If we consider only twovariables, say, the quality of work and the fee paid to be influencing eachother and the effect of the other influencing variable is kept constant then itis a problem of partial correlation.
Linear and non-linear (curvilinear)correlation:- if the amount of change in onevariable tends to bear a constant ratio with the amount of change in the otherthen the correlation is said to be linear. If we draw a graph with one variableon X-axis and the other on Y-axis then almost all the point will approximatelyfall on a line. If amount of change in one variable does not bear a constantratio with the amount of change in the other then the correlation is said to benon-linear. In most of the practical situations we find a non-linearrelationship between the variables. But the techniques of analysis formeasuring non-linear correlation are far more complicated than those for linearcorrelation. Therefore, we generally make an assumption that the relationbetween the variables is of linear type.
