Question

which of the following regressions represents the weakest linear relationship between x and y? regression 1 y = ax + b a = -9.7 b = -13.8 r = -0.0889 regression 2 y = ax + b a = 1.4 b = -9.4 r = 0.3115 regression 3 y = ax + b a = 16.4 b = -3 r = 0.0238 regression 4 y = ax + b a = -14.8 b = -1.7 r = -0.5266 answer: regression 1 regression 2 regression 4

Explanation:

Step1: Recall correlation - coefficient concept

The absolute - value of the correlation coefficient $r$ measures the strength of the linear relationship. The closer $|r|$ is to 0, the weaker the linear relationship.

Step2: Calculate absolute - values of given $r$ values

For Regression 1: $|r_1|=|-0.0889| = 0.0889$; for Regression 2: $|r_2|=|0.3115| = 0.3115$; for Regression 3: $|r_3|=|0.0238| = 0.0238$; for Regression 4: $|r_4|=|-0.5266| = 0.5266$.

Step3: Compare absolute - values

We compare the values: $0.0238<0.0889<0.3115<0.5266$. Since the absolute - value of $r$ for Regression 3 is the smallest, Regression 3 has the weakest linear relationship.

Answer:

Regression 3