Correlation can be explained as a single number which describes the extent of relationship between two variables. The relationship between these two variables is described through a single value, which is the coefficient.
Correlation coefficient ‘r’ is a number that represents the level of relationship between two individual variables (Washington et al, 2010). For instance, correlation coefficient can assist in identifying the relationship between consumer age groups and type of atmosphere in a restaurant they enjoy the most. Similarly, the correlation coefficient can be used to establish the nature of relationships between consumer genders, and the level of their interests in European cuisine.
The coefficient of correlation is expressed by the formula:
The range of value ‘r’ can take changes from +1 to -1 depending on the type of correlation. Specifically,
a) The correlation would be perfectly positive if ‘r’ is equal to +1;
b) The correlation would be perfectly negative if ‘r’ is equal to -1;
c) The relationship between the two variables would be considered to be uncorrelated if ‘r’ is equal to zero.
Other forms of correlation include Pearson Product-Moment, Spearman Rank, Lagged, Autocorrelation and others.
The Pearson product-moment correlation is calculated by taking the ratio of the sample of the two variables to the product of the two standard deviations and illustrates thestrength of linear relationships. In Pearson product-moment correlation the correlation coefficient is not robust due to the fact that strong linear relationships between the variables are not recognized. The correlation coefficient is sensitive to outlying points therefore the correlation coefficient is not resistant.
Spearman Rank correlation requires the data to be sorted and the value to be assigned a specific rank with 1 to be assigned as the lowest value. Moreover, in case of data value appearing more than once, equal values will be specified their average rank.
Autocorrelation (serial correlation) implies the correlation among the values of the same variables but at various times, the coefficient of which is calculated by changing lagged data with the formula for the Pearson product-moment correlation coefficient. Also, because a series of unshifted data will express perfect correlation, the function begins with the coefficient of 1.