Question

how is a linear relationship between two variables measured in statistics? explain.
select all the true statements.
there are several numerical measures of correlation, called correlation coefficients.
the correlation coefficient ranges from -1 to 1. values closer to 0 show a strong linear relationship.
the correlation coefficient ranges from -1 to 1. values close to +1 or -1 show a strong linear relationship.
if the values of x and y are interchanged, the correlation coefficient remains the same.
the value of the coefficient is resistant to outliers.

Explanation:

• Statement A is true: Correlation coefficients (e.g., Pearson, Spearman) are numerical measures of correlation.
• Statement B is false: Values closer to 0 indicate weak linear relationships, not strong.
• Statement C is true: The coefficient ranges from -1 (perfect negative linear) to 1 (perfect positive linear); values near these extremes mean strong linear relationships.
• Statement D is true: Correlation is symmetric, so swapping x and y does not change the coefficient.
• Statement E is false: Correlation coefficients (especially Pearson) are sensitive to outliers, not resistant.

Answer:

A. There are several numerical measures of correlation, called correlation coefficients., C. The correlation coefficient ranges from -1 to 1. Values close to +1 or -1 show a strong linear relationship., D. If the values of x and y are interchanged, the correlation coefficient remains the same.