Final answer:
Positive values of covariance indicate a positive relation between the x and the y variables, where an increase in one variable is associated with an increase in the other, and a decrease in one is related with a decrease in the other. The correct option is d.
Step-by-step explanation:
Positive values of covariance indicate a positive relation between the x and the y variables. This concept is integral to understanding correlation, which measures the strength and direction of a linear relationship between two variables. A positive correlation coefficient, denoted as r, signifies that as one variable increases, the other variable tends to increase as well, and when one variable decreases, the other variable tends to decrease.
This relationship is evident in a scatter plot where data points with a positive correlation will cluster around a line with a positive slope. The correlation coefficient can range between -1 and +1, and the closer it is to +1, the stronger the positive linear relationship between the variables. Conversely, a negative correlation indicates that the variables move in opposite directions, and a correlation coefficient of 0 indicates no linear relationship.
The standard deviation, while always positive or zero, does not directly relate to the sign of the correlation but rather to the spread of individual data points around the mean of the data set.
Hence, Option d is correct.