Question

functions and lines linear relationship and the correlation coefficient. answer the questions that follow. the same response may be the correct answer for more than one question. 1. which data - set indicates the strongest linear relationship between its two variables? 2. which data - set has an apparent negative, but not perfect, linear relationship between its two variables? 3. for which data - set does the correlation coefficient r

Explanation:

Step1: Understand linear - relationship strength

The closer the data points are to a straight - line pattern, the stronger the linear relationship. In Figure 3, the data points are tightly clustered around an imaginary straight line.

Step2: Identify negative linear relationship

A negative linear relationship means as one variable increases, the other decreases. In Figure 2, the data points generally trend downwards from left to right, indicating a negative but not perfect linear relationship.

Step3: Recall correlation coefficient concept

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. A strong linear relationship (either positive or negative) has a value of \(r\) close to \(- 1\) or \(1\). Since Figure 3 has the strongest linear relationship, its \(r\) value is closest to \(-1\) or \(1\).

Answer:

1. The data set in Figure 3
2. The data set in Figure 2
3. The data set in Figure 3