Question

which of the following regressions represents the strongest positive linear relationship bet x and y?
regression 1
$y = ax + b$
$a = -16.6$
$b = -18.5$
$r = -0.9962$
regression 2
$y = ax + b$
$a = 4.8$
$b = -2.4$
$r = 0.8167$
regression 3
$y = ax + b$
$a = 2.1$
$b = -15$
$r = 1.0745$
regression 4
$y = ax + b$
$a = 11.3$
$b = 1.8$
$r = 0.0104$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. For a positive linear relationship, \(r> 0\). Also, \(|r|\) should be as close to \(1\) as possible.

Step2: Analyze each regression

• Regression 1: \(r=-0.9962\) (negative relationship, so not valid for positive)
• Regression 2: \(r = 0.8167\) (positive, \(|r|=0.8167\))
• Regression 3: \(r = 1.0745\) (not possible as \(|r|\leq1\))
• Regression 4: \(r=0.0104\) (positive but \(|r|\) is very small)

Answer:

Regression 2