Identify the true statements about the correlation coefficient, r.

Question

a. When the data points in a scatter plot fall closely around a straight line that is either increasing or decreasing, the correlation between the two variables is strong.

 

b. A correlation coefficient of zero means that no relationship exists between the two variables.

 

c. If two variables are negatively correlated, when one variable increases, the other variable also increases.

 

d. The value of ? ranges from negative one to positive one.

 

e. The absolute value of ? describes the magnitude of the association between two variables.

 

f. The correlation coefficient is not affected by outliers.

Answer 1

Assuming "?" means the coefficient r, here are your answers:

a. This is vague, since a strong-positive and weak-positive correlation are both technically "increasing" (positive slope). Similarly for negative correlation. Speaking in a strict true/false, I would label this is False.

b. Again, this is a bit tricky. When "r" is 0, it means that there is no linear correlation evident. It doesn't mean that there are no correlations between the variable. If this is an introductory stats course, the answer is probably True. Otherwise, False.

c. This is straightforward. Negative coefficients indicate an opposite relationship. As one increases, the other decreases (or visa versa). False.

d. The coefficient r is between [0,1] (inclusive), not (0,1). So, if that wording indicates [0,1], then True.

e. Straightforward True

f. Straightforward, False. The correlation coefficient is very sensitive to outliers.