Question

which of the following regressions represents the weakest linear relationship between x and y?
regression 1
$y = ax + b$
$a = -7.6$
$b = -5.8$
$r = -0.1024$
regression 2
$y = ax + b$
$a = 3.9$
$b = 11.9$
$r = 0.9999$
regression 3
$y = ax + b$
$a = 19.7$
$b = 5.6$
$r = 0.4079$
regression 4
$y = ax + b$
$a = -10.9$
$b = -8.9$
$r = -0.4494$
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: \(|r| = |- 0.1024|=0.1024\)
• For Regression 2: \(|r| = |0.9999| = 0.9999\)
• For Regression 3: \(|r|=|0.4079| = 0.4079\)
• For Regression 4: \(|r|=|-0.4494| = 0.4494\)

Step3: Compare the absolute values

We have \(0.1024<0.4079<0.4494<0.9999\)

Answer:

Regression 1