Question

Which of the following statements are true? select all that apply.

1)The correlation coefficient gives us information as to how strong the linear association is between two quantitative variables
2) The Correlation coefficient has units of measurement and does always lie between -1.0 and +1.0
3) The closer the absolute value of r is to 1, the stronger the relationship is between the two variables.
4) A correlation coefficient of r=0 indicates a strong linear relationship between two variables.
5) A correlation coefficient of r=-0.9 indicates a weak linear relationship between two variables
6) Two variables can be correlated without one causing the other

Answer 1

True statements about the correlation coefficient are that it gives us information about the strength of the linear association between two variables (1), the closer the absolute value of r is to 1, the stronger the relationship (3), and that correlation does not imply causation, meaning variables can be correlated without one causing the other (6).

Step-by-step explanation:

The question pertains to the characteristics of the correlation coefficient, commonly denoted as r, and its interpretation in statistical analysis. The correlation coefficient is a measure of the linear relationship between two quantitative variables, and it ranges from -1 to 1. Let's address the statements provided:

1. The correlation coefficient gives us information as to how strong the linear association is between two quantitative variables. True.
2. The Correlation coefficient has units of measurement and does always lie between -1.0 and +1.0. False, r is unitless and does always lie between -1.0 and +1.0.
3. The closer the absolute value of r is to 1, the stronger the relationship is between the two variables. True.
4. A correlation coefficient of r=0 indicates a strong linear relationship between two variables. False, r=0 indicates no linear relationship.
5. A correlation coefficient of r=-0.9 indicates a weak linear relationship between two variables. False, r=-0.9 indicates a strong linear relationship, but in a negative direction, meaning as one variable increases, the other decreases.
6. Two variables can be correlated without one causing the other. True, correlation does not imply causation.

It is essential to remember that a correlation coefficient close to -1 or 1 signifies a strong linear relationship, while a coefficient close to 0 signifies a weak or no linear relationship. The sign of the coefficient indicates the direction of the relationship; positive for a direct relationship and negative for an inverse relationship.

Answer 2

1, 3 and 6

Step-by-step explanation:

Correlation coefficient denoted as r tells us about the Linear Relationship between two quantitative variables. The value of r always lies between -1 and 1. It is a unit-less quantity.

If the absolute value of correlation coefficient is closer to 1 it indicates a strong Linear relationship between two variables. If the absolute value of r is closer to 0 it indicates a weak Linear Relationship between two variables.

Therefore,

Statement 1 is true.

Statement 2 is False as correlation coefficient has no units.

Statement 3 is true.

Statement 4 is false. As r = 0 indicates no linear relationship at all.

Statement 5 is false. The absolute value of r is close to 1 so it indicates a strong linear relationship

Statement 6 is true. Correlation does not imply causation. This means the two variable may or may not be causing each other but still be co-related.