Question

match the linear correlation coefficient to the scatter diagram. the scales on the x - and y - axes are the same for each diagram(a) ( r=-0.933 )(b) ( r=-0.038 )(c) ( r=-0.523 )(d) ( r=-1 )click the icon to view the scatter diagrams.(b) identify the scatter diagram corresponding to ( r=-0.038 ). choose the correct answer

Explanation:

Step1: Understand the nature of the correlation coefficient

The linear correlation coefficient \(r\) measures the strength and direction of a linear relationship. A value of \(r = - 0.038\) is close to \(0\), indicating a very weak negative linear relationship.

Step2: Analyze the scatter - diagrams

A scatter - diagram with \(r=-0.038\) should have points that are very loosely scattered. There should be no clear pattern of a negative linear trend (unlike \(r = - 0.933\) which is a strong negative linear relationship, \(r=-0.523\) which is a moderate negative linear relationship and \(r = - 1\) which is a perfect negative linear relationship).

Answer:

The scatter - diagram with the most loosely scattered points (showing a very weak negative linear relationship) corresponds to \(r=-0.038\).