The coefficient of correlation is independent of

Options

A. change of scale only
B. change of origin only
C. both change of scale and change of origin
D. neither change of scale nor change or origin

Answer

To solve the question regarding the coefficient of correlation and its independence from certain changes, let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Coefficient of Correlation**:
The coefficient of correlation (denoted as \( r \)) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1.

**Hint**: Remember that \( r \) indicates how closely two variables are related.

2. **Identifying Changes**:
- **Change of Scale**: This refers to multiplying or dividing all values of a variable by a constant. For example, if we multiply all values of \( X \) by a factor \( k \), the relationship between \( X \) and \( Y \) remains unchanged in terms of correlation.
- **Change of Origin**: This involves adding or subtracting a constant from all values of a variable. For example, if we add a constant \( c \) to all values of \( X \), the correlation remains the same.

**Hint**: Think of how scaling (multiplying/dividing) and shifting (adding/subtracting) affects the data.

3. **Independence of Correlation**:
The coefficient of correlation is independent of both change of scale and change of origin. This means that regardless of whether we scale or shift the data, the value of the correlation coefficient \( r \) will not change.

**Hint**: Consider how the relative positions of points in a scatter plot remain the same under these transformations.

4. **Conclusion**:
Since the coefficient of correlation does not change with either transformation, the correct answer to the question is that it is independent of both change of scale and change of origin.

**Final Answer**: The coefficient of correlation is independent of both change of scale and change of origin.