Question

The strength of a linear association between two quantitative variables can be measured by the:

• A. Regression coefficient
• B. Correlation coefficient
• C. Standard deviation
• D. Coefficient of variance

Hint:

Remember that while a high absolute value of the correlation coefficient indicates a strong linear relationship, its sign (positive or negative) also provides information about the direction of the relationship.

Answer 1

The Correct Option is B

Step 1: Concept
The strength and direction of a linear relationship between two quantitative variables can be quantitatively assessed using the correlation coefficient.

Step 2: Meaning
A correlation coefficient is a statistical measure that indicates the extent to which two or more variables fluctuate together. The value ranges from -1 to 1, where -1 represents a perfect negative linear relationship, 0 indicates no linear relationship, and 1 signifies a perfect positive linear relationship.

Step 3: Analysis
Regression Coefficient (A): This measures the change in the dependent variable for each unit increase in the independent variable. While it is useful for predicting outcomes based on the regression line, it does not directly measure the strength of the association. Correlation Coefficient (B): This specifically quantifies both the direction and the strength of a linear relationship between two variables. It ranges from -1 to 1, making it an ideal measure for assessing the strength of a linear association. Standard Deviation (C): This measures the dispersion or spread of data points around the mean. While important in understanding variability, it does not indicate the strength of the linear relationship between two variables. Coefficient of Variance (D): This is used to measure relative variability and is defined as the ratio of the standard deviation to the mean. It is not a direct measure of the strength of a linear association between two quantitative variables.

Step 4: Conclusion
The correlation coefficient effectively captures both the direction and the strength of the linear relationship between two quantitative variables, making it the most appropriate choice for measuring the strength of such an association. Final Answer: (B)