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 strength of a linear relationship is determined by the absolute value of the correlation coefficient \( r \). 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

We compare \( 0.9373\), \(0.8865\), \(0.6453\) and \(0.7281\). Since \(0.6453<0.7281 < 0.8865<0.9373\)

Answer:

Regression 3