Question

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 3
regression 2
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 - value of each $r$

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 have $0.3089<0.6017<0.7329<0.8607$. Since the $|r|$ value for Regression 2 is the smallest among them, Regression 2 represents the weakest linear relationship.

Answer:

Regression 2