Question

which of the following regressions represents the strongest linear relationship between x and y?
regression 1
$y = ax + b$
$a = -18.6$
$b = -12.4$
$r = -0.6579$
regression 2
$y = ax + b$
$a = -8.5$
$b = 11$
$r = -1.155$
regression 3
$y = ax + b$
$a = -12.5$
$b = 2.2$
$r = -0.4319$
regression 4
$y = ax + b$
$a = 7.6$
$b = -9$
$r = 0.3107$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

Step1: Recall the property of the correlation coefficient \(r\)

The strength of a linear relationship is determined by the absolute value of the correlation coefficient \(r\), \(|r|\). The closer \(|r|\) is to \(1\), the stronger the linear relationship.

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

• For Regression 1: \(|r| = |- 0.6579|=0.6579\)
• For Regression 2: Since \(|r|\leq1\), \(r = - 1.155\) is invalid (out of the range \([-1,1]\))
• For Regression 3: \(|r|=|-0.4319| = 0.4319\)
• For Regression 4: \(|r|=|0.3107|=0.3107\)

Answer:

Regression 1