Question

The coefficient of correlation is independent of

• A. Change of scale only
• B. Change of origin only
• C. Both change of scale & origin
• D. No change

Hint:

The coefficient of correlation remains unchanged under linear transformations, meaning it is scale and origin invariant.

Answer 1

The Correct Option is C

The coefficient of correlation, often denoted as \( r \), is a measure of the linear relationship between two variables. It is calculated as:

\[ r = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{\sqrt{[n \Sigma x^2 - (\Sigma x)^2][n \Sigma y^2 - (\Sigma y)^2]}} \]

Where \( x \) and \( y \) are the two variables, and \( n \) is the number of data points.

The important point to note is that the coefficient of correlation is **independent** of both the scale (i.e., the units of the variables) and the origin (i.e., the reference point for measuring the variables). This means that the coefficient of correlation will remain the same if you change the units of measurement or shift the origin of the data.

Thus, the correct answer is option (C): Both change of scale & origin.