Question

which of the following regressions represents the strongest negative linear relationship between x and y? regression 1 y = ax + b a = -11.6 b = 6.2 r = -0.4625 regression 2 y = ax + b a = -4.8 b = -4.3 r = -0.896 regression 3 y = ax + b a = -4.3 b = -13.3 r = -1.0151 regression 4 y = ax + b a = 15.4 b = 2.5 r = 0.964 answer regression 1 regression 3 regression 2 regression 4

Explanation:

Step1: Recall correlation - coefficient concept

The correlation - coefficient $r$ measures the strength and direction of a linear relationship. For a negative linear relationship, the closer the value of $r$ is to - 1, the stronger the negative linear relationship.

Step2: Analyze each regression's $r$ value

Regression 1 has $r=-0.4625$, Regression 2 has $r = - 0.896$, Regression 3 has an invalid $r=-1.0151$ (since $-1\leq r\leq1$), and Regression 4 has a positive $r = 0.064$.

Answer:

Regression 2