Question

which of the following regressions represents the weakest linear relationship between x and y? regression 1 $y = ax + b$ $a = -3.8$ $b = -7.3$ $r = -0.8516$ regression 2 $y = ax + b$ $a = 19.7$ $b = 13.2$ $r = 0.1204$ regression 3 $y = ax + b$ $a = -10$ $b = -6.1$ $r = -0.8836$ regression 4 $y = ax + b$ $a = 1.8$ $b = 4.6$ $r = 0.3766$ answer regression 1 regression 2 regression 3 regression 4 submit answer

Explanation:

Step1: Recall the concept of correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. The closer \(|r|\) is to \(1\), the stronger the linear relationship. The closer \(|r|\) is to \(0\), the weaker the linear relationship.

Step2: Calculate the absolute values of \(r\) for each regression

• For Regression 1: \(|r| = |- 0.8516|=0.8516\)
• For Regression 2: \(|r| = |0.1204| = 0.1204\)
• For Regression 3: \(|r|=|-0.8836| = 0.8836\)
• For Regression 4: \(|r|=|0.3766|=0.3766\)

Step3: Compare the absolute values

We compare \(0.8516\), \(0.1204\), \(0.8836\), and \(0.3766\). Since \(0.1204<0.3766 < 0.8516<0.8836\)

Answer:

Regression 2