Question

which of the following regressions represents the weakest linear relationship between x and y?
regression 1
$y = ax + b$
$a = - 18.5$
$b = 10.5$
$r = - 0.9373$
regression 2
$y = ax + b$
$a = 18.6$
$b = 3.9$
$r = 0.8865$
regression 3
$y = ax + b$
$a = - 11.6$
$b = - 16.4$
$r = - 0.6453$
regression 4
$y = ax + b$
$a = - 4.5$
$b = - 10.2$
$r = - 0.7281$
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 \(1\), the stronger the 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: \(|r| = |- 0.9373|=0.9373\)
For Regression 2: \(|r| = |0.8865| = 0.8865\)
For Regression 3: \(|r|=|-0.6453| = 0.6453\)
For Regression 4: \(|r|=|-0.7281|=0.7281\)

Step3: Compare the absolute values

Since \(0.6453<0.7281<0.8865<0.9373\)

Answer:

Regression 3