Question

order the correlation coefficients from weakest to strongest negative correlation. -0.37 -0.82 -0.59 -0.18

Explanation:

Step1: Understand the property of negative correlation coefficients

The closer a negative correlation coefficient is to \(0\), the weaker the negative correlation. The closer it is to \(- 1\), the stronger the negative correlation.

Step2: Compare the magnitudes of the given coefficients

We have the coefficients \(-0.37\), \(-0.82\), \(-0.59\), \(-0.18\).
The magnitudes are \(| - 0.18|=0.18\), \(| - 0.37| = 0.37\), \(| - 0.59|=0.59\), \(| - 0.82|=0.82\)

Step3: Order the coefficients based on the magnitude (for negative values)

Since for negative numbers \(a,b\), if \(|a|<|b|\), then \(a > b\). So ordering from weakest (closest to \(0\)) to strongest (closest to \(-1\)): \(-0.18\), \(-0.37\), \(-0.59\), \(-0.82\)

Answer:

\(-0.18\), \(-0.37\), \(-0.59\), \(-0.82\)