Question

which of the following regressions represents the strongest linear relationship between x and y?
regression 1
$y = ax + b$
$a = 17.1$
$b = - 3.2$
$r = 0.0241$
regression 2
$y = ax + b$
$a = 7.6$
$b = - 1.3$
$r = 1.1543$
regression 3
$y = ax + b$
$a = 12.4$
$b = - 4.4$
$r = 0.1826$
regression 4
$y = ax + b$
$a = - 6.9$
$b = - 8.3$
$r = - 0.7301$
answer
regression 1
regression 3
regression 2
regression 4

Explanation:

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

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. The value of \(r\) lies in the interval \([- 1,1]\). The closer \(|r|\) is to \(1\), the stronger the linear relationship.

Step2: Analyze the given \(r\) values

For Regression 1: \(|r|=|0.0241| = 0.0241\)
For Regression 2: \(r = 1.1543\) (invalid since \(r\in[-1,1]\))
For Regression 3: \(|r|=|0.1826|=0.1826\)
For Regression 4: \(|r|=|-0.7301| = 0.7301\)

Answer:

Regression 4