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

Explanation:

Step1: Recall correlation - coefficient concept

The strength of a linear relationship is determined by the absolute - value of the correlation coefficient \(r\). The closer \(|r|\) is to 0, the weaker the linear relationship.

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

For Regression 1: \(|r_1|=|- 0.8516| = 0.8516\).
For Regression 2: \(|r_2|=|0.1204| = 0.1204\).
For Regression 3: \(|r_3|=|-0.8836| = 0.8836\).
For Regression 4: \(|r_4|=|0.3766| = 0.3766\).

Step3: Compare absolute - values

We compare \(0.8516\), \(0.1204\), \(0.8836\), and \(0.3766\). We find that \(0.1204\) is the smallest among them.

Answer:

Regression 2