Question

which of the following regressions represents the strongest linear relationship between x and y?
regression 1
$y = ax + b$
$a = -11.8$
$b = 18.7$
$r = -0.3856$
regression 2
$y = ax + b$
$a = 7.2$
$b = -18.6$
$r = 1.0833$
regression 3
$y = ax + b$
$a = -12.3$
$b = 4.6$
$r = -0.596$
regression 4
$y = ax + b$
$a = -7.3$
$b = 17.6$
$r = -0.4375$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

Step1: Recall the rule 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.

Step2: Calculate absolute values of \(r\) for each regression

• For Regression 1: \(|r| = |- 0.3956|=0.3956\)
• For Regression 2: \(|r| = |1.0833|\). But \(r = 1.0833\) is invalid since \(|r|\leq1\).
• For Regression 3: \(|r| = |-0.596| = 0.596\)
• For Regression 4: \(|r|=|-0.4375| = 0.4375\)

Answer:

Regression 3