Question

question which of the following regressions represents the weakest linear relationship between x and y? regression 1 y = ax + b a = -11.4 b = 13.9 r = -0.9873 regression 2 y = ax + b a = -2.8 b = 14.6 r = -0.866 regression 3 y = ax + b a = -3 b = -18 r = -0.3575 regression 4 y = ax + b a = -13.9 b = 7 r = -0.8712 answer regression 1 regression 3 regression 2 regression 4

Explanation:

Step1: Recall correlation - coefficient concept

The correlation - coefficient $r$ measures the strength of the 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 absolute - values of $r$ for each regression

For Regression 1: $|r_1| = | - 0.9873|=0.9873$.
For Regression 2: $|r_2| = | - 0.866| = 0.866$.
For Regression 3: $|r_3| = | - 0.3575|=0.3575$.
For Regression 4: $|r_4| = | - 0.8712| = 0.8712$.

Step3: Compare absolute - values

Among $0.9873$, $0.866$, $0.3575$, and $0.8712$, the smallest value is $0.3575$ which corresponds to Regression 3.

Answer:

Regression 3