Simple, Partial and Multiple Correlation: Whether the correlation is simple, partial or multiple depends on the number of variables studied. The correlation is said to be simple when only two variables are studied. The correlation is either multiple or partial when three or more variables are studied. The correlation is said to be Multiple when three variables are studied simultaneously. Such as, if we want to study the relationship between the yield of wheat per acre and the amount of fertilizers and rainfall used, then it is a problem of multiple correlations.
Whereas, in the case of a partial correlation we study more than two variables, but consider only two among them that would be influencing each other such that the effect of the other influencing variable is kept constant. Such as, in the above example, if we study the relationship between the yield and fertilizers used during the periods when certain average temperature existed, then it is a problem of partial correlation.