Which of the following statements regarding the coefficient of correlation is true?
Click on the arrows to vote for the correct answer
A. B. C. D. E.D
All of these answers are properties of the coefficient of correlation. Make sure you know the formula for the coefficient of correlation.
The correct answer is D. All of these answers.
The coefficient of correlation, also known as the correlation coefficient or simply correlation, is a statistical measure that quantifies the strength and direction of the relationship between two variables. It is represented by the symbol "r."
Here's a detailed explanation of each statement:
A. It ranges from -1.0 to +1.0 inclusive: The correlation coefficient ranges from -1.0 to +1.0, inclusive. A correlation of +1.0 indicates a perfect positive linear relationship between the variables, meaning that as one variable increases, the other variable also increases proportionally. On the other hand, a correlation of -1.0 indicates a perfect negative linear relationship, where one variable decreases as the other variable increases. A correlation coefficient of 0 indicates no linear relationship between the variables.
B. A value of 0.00 indicates two variables are not related: If the correlation coefficient is 0, it indicates that there is no linear relationship between the two variables being analyzed. However, it's important to note that this does not necessarily mean there is no relationship at all. There could still be a nonlinear relationship or some other form of association between the variables.
C. None of these answers: This answer is incorrect since both statements A and B are true.
D. All of these answers: This is the correct answer because statements A and B are both true. The correlation coefficient does range from -1.0 to +1.0 inclusive, and a value of 0.00 does indicate that two variables are not related.
E. It measures the strength of the relationship between two variables: This statement is true. The correlation coefficient measures the strength of the linear relationship between two variables. A correlation coefficient close to +1.0 or -1.0 indicates a strong linear relationship, while a correlation coefficient closer to 0 indicates a weak or no linear relationship.
In summary, the coefficient of correlation measures the strength and direction of the linear relationship between two variables, and it ranges from -1.0 to +1.0 inclusive. A value of 0.00 indicates no linear relationship, and therefore the correct answer is D. All of these answers.