Question

shown below are the scatter plots for four different data sets. answer the questions that follow. the same response may be the correct answer for more than one question. 1. which data set shows the least evidence of a linear relationship? 2. for which data set does the correlation coefficient r

Explanation:

Step1: Understand linear - relationship in scatter - plots

A linear relationship in a scatter - plot is indicated by points that roughly form a straight - line pattern. The less the points form a straight - line pattern, the less evidence of a linear relationship.

Step2: Analyze each figure

In Figure 1, the points are randomly scattered and do not form any discernible straight - line pattern. In Figure 2, there is a slight negative linear trend. In Figure 3, there is a clear positive linear trend. In Figure 4, the points are also randomly scattered. But Figure 1 has a more dispersed and less organized set of points compared to Figure 4.

Step3: Recall correlation coefficient concept

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. \(r = 1\) indicates a perfect positive linear relationship, \(r=- 1\) indicates a perfect negative linear relationship, and \(r = 0\) indicates no linear relationship.

Step4: Identify data set for \(r\approx1\)

For a correlation coefficient \(r\) to be close to 1, the data points should form a strong positive linear trend. Figure 3 shows a strong positive linear trend where the points closely follow an upward - sloping straight - line pattern.

Answer:

1. Figure 1
2. Figure 3