The correlation between height and armspan in a sample of...

The correlation between height and armspan in a sample of adult women was found to be $r=0.948 .$ The correlation between arm span and height in a sample of adult men was found to be $r=0.868$. Assuming both associations are linear, which association-the association between height and arm span for women, or the association between height and arm span for men-is stronger? Explain.

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Key Concepts

Correlation Coefficient

The correlation coefficient quantifies the degree to which two variables are linearly related, ranging from -1 to +1. A value closer to +1 or -1 indicates a stronger linear relationship, while a value near 0 suggests a weak linear relationship.

Linear Association

A linear association implies that the relationship between two variables can be represented by a straight line. This means that changes in one variable are associated with proportional changes in the other variable.

Strength of Association

The strength of association refers to how closely the data points cluster around a line in a scatterplot. A higher absolute value of the correlation coefficient indicates a stronger association between the variables.

Comparing Correlations

When comparing correlations, the magnitude of the correlation coefficients is used. A higher absolute value indicates a stronger linear relationship, meaning that one pair of variables has a more tightly coupled relationship than another.

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