The coefficient of correlation, also known as Pearson's correlation coefficient, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

The statement "the value of the coefficient of correlation is unaffected by a change of origin" refers to the fact that shifting or changing the origin of the data does not alter the value of the correlation coefficient. Let's discuss this in more detail:

Position of Origin:
- The position of origin refers to the location of the coordinate system used to represent the data. Shifting the origin does not change the relationship between the variables, as it only changes the reference point for the data.
- For example, if we have a dataset where the x-values are shifted by a certain amount, the correlation coefficient remains the same because the relationship between the variables remains unchanged.

Change of Origin:
- Changing the origin involves adding or subtracting a constant value from all the data points. This shift does not affect the correlation coefficient because it only changes the position of the data along the x and y-axes without altering the relationship between the variables.
- For instance, if we add a constant value to both sets of data, the correlation coefficient remains unchanged because the relative positions of the data points to each other remain the same.

Position of Values:
- The position of values refers to the individual data points and their respective positions within the dataset. The correlation coefficient is unaffected by the specific positions of the data points because it measures the overall linear relationship between the variables, not their individual positions.
- Reordering or rearranging the data points does not change the correlation coefficient as long as the relationship between the variables remains the same.

Change of Values:
- Changing the values of the data points, such as increasing or decreasing their magnitudes, does not directly affect the correlation coefficient. However, it can indirectly influence the correlation coefficient if the change alters the linear relationship between the variables.
- If the change in values preserves the linear relationship, the correlation coefficient remains the same. However, if the change introduces a non-linear relationship or alters the original linear relationship, the correlation coefficient may change.

In summary, the value of the coefficient of correlation is unaffected by the position of origin, position of values, and change of values. The only factor that does not affect the correlation coefficient is a change of origin, which involves shifting the coordinate system without altering the relationship between the variables.