Question

1. If the correlation between two variables X and Y is 0.5, then ... Group of answer choices A. there is no linear relationship between the variables. B. there is an inverse relationship between the variables. C. there is no relationship between the variables. D. there is a direct relationship between the variables.

Answer 1

The correlation coefficient of 0.5 between variables X and Y signifies a moderate direct relationship, as they tend to increase together. The correct answer is that there is a direct relationship between the variables.

Step-by-step explanation:

If the correlation coefficient between two variables X and Y is 0.5, this indicates that there is a direct relationship between the variables. This means as one variable increases, the other variable tends to also increase. However, the strength of this relationship is of moderate magnitude since the correlation coefficient is 0.5, which is halfway between 0 (no correlation) and 1 (perfect positive correlation).

The correct answer to the question is D. there is a direct relationship between the variables X and Y. A correlation coefficient of 0.5 is significantly different from zero, suggesting that there is a significant linear relationship between X and Y, and it is positive because the coefficient is above zero.

Answer 2

The correlation coefficient measures the strength of the linear association between two variables. If the correlation coefficient between two variables X and Y is 0.5, it indicates a positive relationship between the variables.

Step-by-step explanation:

The correlation coefficient, r, measures the strength of the linear association between x and y. The variable r has to be between -1 and +1. When r is positive, x and y tend to increase and decrease together. When r is negative, x increases and y decreases, or the opposite occurs: x decreases and y increases.

The number portion of the correlation coefficient indicates the strength of the relationship. The closer the number is to 1 (be it negative or positive), the more strongly related the variables are, and the more predictable changes in one variable will be as the other variable changes. The closer the number is to zero, the weaker the relationship, and the less predictable the relationships between the variables becomes. For instance, a correlation coefficient of 0.9 indicates a far stronger relationship than a correlation coefficient of 0.3.

If the correlation between two variables X and Y is 0.5, it indicates a positive relationship between the variables. This means that as the values of X increase, the values of Y also tend to increase. However, it is important to note that the correlation coefficient alone does not determine the presence of a causal relationship or indicate the direction of the relationship. It only measures the strength and direction of the linear association between the variables.