Question

question
which of the following regressions represents the strongest negative linear relationship between x and y?
regression 1
$y = ax + b$
$a = 8.4$
$b = - 15$
$r = 0.4413$
regression 2
$y = ax + b$
$a = - 8.2$
$b = - 2.7$
$r = - 0.1255$
regression 3
$y = ax + b$
$a = - 5.6$
$b = - 19.4$
$r = - 0.6047$
regression 4
$y = ax + b$
$a = 18.5$
$b = - 3.9$
$r = 0.8666$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

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

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. For a negative linear relationship, \(r<0\). The closer \(|r|\) is to \(1\), the stronger the linear relationship.

Step2: Analyze each regression

• Regression 1: \(r = 0.4413>0\), so it is a positive linear relationship.
• Regression 2: \(r=- 0.1255\), \(|r|=0.1255\)
• Regression 3: \(r =-0.6047\), \(|r| = 0.6047\)
• Regression 4: \(r = 0.8666>0\), so it is a positive linear relationship.

Since \(0.6047>0.1255\) and we are looking for the strongest negative linear relationship (negative \(r\) value with the largest magnitude among negative \(r\) values)

Answer:

Regression 3