Question

The Pearson correlation coefficient (r) equals one when there is strong linear relationship between x and y.

True/False

Answer 1

Answer: False.

Explanation:

Pearson's Correlation Coefficient

Correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and blood pressure. Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables.

Pearson's correlation coefficient (r) for continuous (interval level) data ranges from -1 to +1:

r = -1		data lie on a perfect straight line with a negative slope
r = 0		no linear relationship between the variables
r = +1		data lie on a perfect straight line with a positive slope

Positive correlation indicates that both variables increase or decrease together, whereas negative correlation indicates that as one variable increases, so the other decreases, and vice versa.

In other words, the values cannot exceed 1.0 or be less than -1.0 whereby a correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.

So we conclude that +1 indicates a perfect positive linear relationship: as one variable increases in its values, the other variable also increases in its values via an exact linear rule.

Hence it is false.