Question

identify the correlation coefficient. which correlation coefficient best describes the relation depicted in the scatter - plot? 0.7 0.1 0 - 0.1 - 0.7

Explanation:

Step1: Recall correlation coefficient properties

The correlation coefficient \(r\) ranges from \(- 1\) to \(1\). A value of \(r = 1\) indicates a perfect positive linear relationship, \(r=-1\) indicates a perfect negative linear relationship, \(r = 0\) indicates no linear relationship. Values close to \(1\) or \(-1\) indicate strong linear relationships, and values close to \(0\) indicate weak linear relationships.

Step2: Analyze the scatter - plot

Looking at the scatter - plot, the points show a general upward trend (from left - to - right), which indicates a positive linear relationship. The points are not too scattered (so the relationship is not extremely weak) but also not perfectly aligned (so \(r
eq1\)). Values of \(r = 0\) (no linear relationship), \(r=-0.1\) and \(r = - 0.7\) (negative relationships) can be eliminated. A value of \(r = 0.1\) would imply a very weak positive relationship, but the scatter - plot shows a relatively stronger positive trend compared to what \(r = 0.1\) would represent. A value of \(r=0.7\) is a reasonable estimate for a moderately strong positive linear relationship as depicted in the scatter - plot.

Answer:

\(0.7\)