Question

Define partial and semi partial correlation and describe the difference between them. Give an example of each.

Answer 1

Solution:

Partial correlation measures the strength of relationship between two variables, while controlling the effect of one or more other variables.

If r12.3 is the correlation between variable x1 and x2 keeping x3 constant.

r13 is the correlation between variables x1 and x3.

Then Partial correlation mathematical formula is as follows:

Example: Relationship between demand of coffee and tea keeping prices of tea constant.

Semipartial correlation measures the strength of linear relationship between two variables x1 and x2 holding third variable x3 constant for just x1 or x2.

If r1(2.3) is the semipartial correlation between variable x1 and x2 where x3 is constant for x2 and r2(1.3) is the semipartial correlation between variable x1 and x2 where x3 is constant for x1 then mathematical formula is as follows:

Difference between partial and semipartial correlation.

Partial correlation holds variable x3 constant for both the other two variable. Whereas, semipartial correlation holds variable x3 for only one variable(either x1or x2).