Question

which of the following regressions represents the weakest linear relationship between x and y? regression 1 y = ax + b a = 12.3 b = 16.9 r = 0.7329 regression 2 y = ax + b a = - 9.5 b = 19.8 r = - 0.3089 regression 3 y = ax + b a = 8.9 b = 12.5 r = 0.8607 regression 4 y = ax + b a = 17.9 b = - 10.5 r = 0.6017 answer regression 1 regression 2 regression 3 regression 4

Explanation:

Step1: Recall the concept of correlation coefficient

The correlation coefficient $r$ measures the strength and direction of a linear relationship. The closer $|r|$ is to 0, the weaker the linear relationship.

Step2: Calculate the absolute - values of $r$ for each regression

For Regression 1: $|r_1| = |0.7329|=0.7329$.
For Regression 2: $|r_2| = | - 0.3089| = 0.3089$.
For Regression 3: $|r_3| = |0.8607| = 0.8607$.
For Regression 4: $|r_4| = |0.6017| = 0.6017$.

Step3: Compare the absolute - values

We compare $0.3089$, $0.6017$, $0.7329$, and $0.8607$. We find that $0.3089$ is the smallest.

Answer:

Regression 2