## Correlation, Applied Statistics

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Correlation

The board of directors of Bata Company is faced with the problem of estimating what the annual sales might be in a shop to be opened in Bagpur where Bata has not operated before. They need this information in order to plan the size of the shop, the amount of stock to be put on the showcase, the number of employees to be hired. An answer to this problem may be found statistically by establishing the general relationship in the cities in which the company is already operating, say between the size of a city’s employed labor force or working population and sales in its Bata shops. From the size of Bagpur’s employed labor force, an estimation of the annual sales in that new shop can be estimated, and the board of directors should be able to base its decision on this estimate.

But the board will also want to know how good this estimate is, since it is based only on a general relationship between sales and employment. Further still, the board may want to compare the relationship existing between sales and labor force on one hand with the relationship existing between sales and number of shops on the other hand. Such problems can be solved through correlation analysis.

Correlation does not deal with one series but rather with the association or relationship between two series and does not measure variation in one series but rather compare variation in two or more series. The existence of correlation between variables does not necessarily mean that one is the cause of the movement in the other. It should be noted that the correlation analysis merely helps in determining the degree of association between two variables, but it does not tell anything about the cause and effect relationship.

Correlation analysis is based on the relationship between two or more variables. The degree of relationship between the variables under consideration is measured through the correlation analysis. The measure of correlation called correlation coefficient, summarizes in one figure the direction and degree of correlation. The direction of change is indicated by + or – signs; the former refers to the movement in the same direction and the latter in the opposite direction; an absence of correlation is indicated by zero. This coefficient ranges between –1 and 1.

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