Question

Since the correlation between the height and weight of this bird species is -0.31, longer birds tend to weigh less than shorter birds by 31%.

a) True
b) False

Answer 1

The statement that a correlation of -0.31 equates to a 31% weight difference in longer birds is incorrect. Correlation coefficients represent the strength and direction of relationships, not direct percentage changes.

Step-by-step explanation:

The student's assertion that a correlation of -0.31 between the height and weight of a bird species means longer birds tend to weigh less than shorter birds by 31% is false. The value -0.31 represents the direction and strength of a linear relationship between two variables. In this case, it indicates a negative correlation between height and weight, meaning that as one variable increases, the other tends to decrease. However, this correlation coefficient does not translate to a direct percentage change. The theory that taller human beings typically weigh more is supported by the fact that humans with bigger bones have more flesh to fill out their frames. This represents a positive correlation. Nevertheless, in the bird species described, the negative correlation found does not mean a precise 31% reduction in weight for longer birds.