Question

The correlation coefficient between packing density and porosity of a set of yarn is

• A. 1
• B. 0
• C. $-1$
• D. Can’t be determined

Hint:

Perfect inverse relationships between two physical parameters always have a correlation coefficient of $-1$.

Answer 1

The Correct Option is C

Step 1: Understanding packing density and porosity.
Packing density represents the fraction of space occupied by fibres in a yarn, whereas porosity represents the fraction of void space present in the yarn structure. Both are complementary structural parameters.
Step 2: Establishing the relationship.
As packing density increases, the void space within the yarn decreases proportionally. Hence, porosity decreases whenever packing density increases, and vice versa.
Step 3: Correlation interpretation.
Since one parameter increases exactly when the other decreases in a linear manner, the relationship is perfectly inverse.
Step 4: Conclusion.
Therefore, the correlation coefficient between packing density and porosity is $-1$.