Let us evaluate each statement to determine whether it is true or false:

1. The sign of the correlation indicates the strength or consistency of the linear relationship between two variables.

   • False. The sign of the correlation indicates the direction of the relationship (positive or negative), not the strength. Strength is determined by the magnitude of the correlation.

2. If the correlation between two variables is –1, it indicates a perfect negative linear relationship between the two variables.

   • True. A correlation of –1 represents a perfect negative linear relationship where all data points lie exactly on a downward-sloping line.

3. The sign of the correlation indicates the direction of the relationship between two variables.

   • True. A positive sign indicates a positive relationship (as one variable increases, the other also increases), and a negative sign indicates a negative relationship (as one variable increases, the other decreases).

4. The correlation is scaleless; that is, it doesn’t change when the measurement units are changed for either or both of the variables.

   • True. Correlation is dimensionless and is not affected by changes in measurement units (e.g., converting inches to centimeters).

5. The correlation indicates the strength and the direction of the linear relationship between two variables.

   • True. Correlation measures both the strength (magnitude) and the direction (sign) of the linear relationship.

6. Correlation measures and describes the behavior of a single variable.

   • False. Correlation describes the relationship between two variables, not the behavior of a single variable.

7. If the correlation between two variables is close to 1, there is a positive linear relationship between the two variables.

   • True. A correlation close to 1 indicates a strong positive linear relationship.

Correct Statements:

• 2, 3, 4, 5, 7

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Would you like further explanation of these points or examples?
Here are 5 related questions to explore further:

1. How is correlation different from causation?
2. Can a non-linear relationship have a high correlation?
3. What are the limitations of using correlation as a measure of association?
4. How does correlation differ from covariance?
5. What are some real-world examples where correlation is used?

Tip: Always visualize data when analyzing correlation to better understand its relationship, as the numerical value of correlation might not reveal non-linear patterns.