Final answer:
Variance cannot be negative because it is calculated as the average of the squared differences from the mean. Covariance and the correlation coefficient can be negative, and E(r) can also be negative depending on the context.
Step-by-step explanation:
Out of the given statistics, variance cannot be negative. Variance, which is denoted by the symbol σ² for a population or s² for a sample, is a measure of the dispersion of a set of data points. It calculates the average of the squared differences from the mean and, since squaring any real number will always result in a non-negative number, variance cannot be negative; it is either positive or zero.
On the other hand, covariance can be positive, negative, or zero, indicating the direction of the linear relationship between variables. The correlation coefficient (r) can vary from -1 to 1, showing both the strength and direction of a linear relationship between two variables. E(r), which often stands for the expected return in finance, can also be positive or negative.
When discussing the correlation coefficient, a value close to 1 or -1 indicates a strong relationship, while a value close to 0 indicates a weak relationship. A positive correlation exists when variables move in the same direction, and a negative correlation occurs when variables move in opposite directions. Therefore, the correlation coefficient indicates the weakest relationship when it is closest to 0.