Question

Which of the following statement about the correlation coefficient r are true?

A. The correlation and the slope of the regression line have the same sign.
B. A correlation of -.35 and a correlation of +.35 show the same strength of clustering around the regression line. C. When r=1, there is a perfect cause-and-effect relationship between the variables.
1. B and C only
2. A and C only
3. A, B, and C
4. A and B only

Answer 1

The correlation coefficient, r, measures the strength of the linear association between x and y. A negative correlation means that x increases, y decreases, or vice versa. A correlation of -.35 and a correlation of +.35 do not show the same strength of clustering around the regression line. When r=1, there is a perfect positive correlation, but it does not imply a perfect cause-and-effect 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 sign of r is the same as the sign of the slope, b, of the best-fit line.

A correlation of -.35 means a negative relationship, while a correlation of +.35 means a positive relationship. However, they do not show the same strength of clustering around the regression line. A correlation of +.35 indicates a weaker clustering around the line compared to a correlation of -.35.

When r=1, there is a perfect positive correlation, but it does not imply a perfect cause-and-effect relationship between the variables. Correlation does not suggest causation.