Question

Why does the correlation coefficient (r) require normal distribution and homoscedastic data?

Answer 1

Solution:

Given that,

A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another. In positively correlated variables, therefore, the value increases or decreases in tandem.

Correlation coefficients are expressed as between plus one  and minus one.

The assumptions are as follows:

level of measurement , linearity, absence of outliers, related pairs, absence of outliers, normality of variables, linearity, and homoscedasticity.

Pearson's correlation is a measure of the linear relationship between two continuous random variables.The distribution of either correlation coefficient will depending on the underlying distribution, although both are asymptotically normal because the central limit theorem.