Question

which of the following regressions represents the weakest linear relationship between x and y? regression 1 y = ax + b a = 8.8 b = -12.5 r = 0.5972 regression 2 y = ax + b a = -11.6 b = -12.9 r = -0.5185 regression 3 y = ax + b a = 11.6 b = 0.1 r = 0.5487 regression 4 y = ax + b a = -12.4 b = 20 r = -0.0443 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: $|r_1|=|0.5972| = 0.5972$.
For Regression 2: $|r_2|=|-0.5185| = 0.5185$.
For Regression 3: $|r_3|=|0.5487| = 0.5487$.
For Regression 4: $|r_4|=|-0.0443| = 0.0443$.

Step3: Compare absolute - values

We compare the values: $0.0443<0.5185<0.5487<0.5972$.

Answer:

Regression 4