Which of the following statements concerning regression and correlation analysis

Question

Which of the following statements concerning regression and correlation analysis is/are true?

A. If the correlation coefficient is zero, then there is no linear relationship between the two variables.
B. A negative value for the correlation coefficient indicates that high values of the independent variable are correlated with low values of the dependent variable.
C. The slope coefficient for a simple linear regression model measures the expected change in the independent variable for a unit change in the dependent variable.

1. Only A

2. Only B

3. Only A and B

4. Only B and C

5. All three statements are false

Explanation / Answer

3. Only A and B

a) True. If the correlation coefficient of two variables is 0, it means that there is no linear relationship between the variables. However, it's true only for a linear relationship; it is possible that they might have a strong curvilinear relationship.

b) True. In case of negative correlation, if one variable increases, the other variable decreases and vice versa. So in other words when x is high, y will be low and vice versa. Same thing is stated in the above option, high values of the independent variable are correlated with low values of the dependent variable.

c) False. The slope represents the change in dependent variable for a unit change in the independent variable changes. The option given states change in x as y changes. But it is change in y as x changes since y is the dependent variable.

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