Correlation is a statistical measure that determines the relationship between two variables. It indicates how changes in one variable are associated with changes in another variable. The correlation coefficient, denoted by 'r', ranges from -1 to +1 and can be interpreted as follows:

- A positive correlation (r > 0) indicates that as one variable increases, the other variable also tends to increase. For example, there may be a positive correlation between studying hours and exam scores.

- A negative correlation (r < 0)="" indicates="" that="" as="" one="" variable="" increases,="" the="" other="" variable="" tends="" to="" decrease.="" for="" example,="" there="" may="" be="" a="" negative="" correlation="" between="" temperature="" and="" />

- A correlation coefficient of 0 (r = 0) indicates no linear relationship between the variables. In other words, there is no association between the variables.

The given statement states that correlation is independent of change of scale. Let's understand what this means:

Explanation:
Change of scale refers to multiplying or dividing all the values of a variable by a constant. It does not affect the correlation between two variables. This is because the correlation coefficient considers the relative positions of the data points rather than their actual values.

For example, let's consider two variables: X and Y. The correlation coefficient between X and Y is calculated using the formula:

r = (Σ((X - X̄)(Y - Ȳ))) / (n * σX * σY)

Where:
- X and Y are the values of the variables
- X̄ and Ȳ are the means of X and Y, respectively
- n is the number of data points
- σX and σY are the standard deviations of X and Y, respectively

Now, if we change the scale of X and Y by multiplying them by a constant, let's say 'c', the new variables become cX and cY. The means and standard deviations also change accordingly, becoming cX̄ and cȲ, and cσX and cσY, respectively.

Plugging these new values into the correlation coefficient formula, we get:

r' = (Σ((cX - cX̄)(cY - cȲ))) / (n * cσX * cσY)

Simplifying this equation, we find that c cancels out from both the numerator and denominator:

r' = (cΣ((X - X̄)(Y - Ȳ))) / (ncσXσY)

This shows that the correlation coefficient remains the same, regardless of the change of scale. Therefore, option D is correct: correlation is independent of change of scale.

In conclusion, correlation measures the relationship between two variables and is not affected by changes in the scale of the variables.