Question

question
which of the following regressions represents the strongest positive linear relationship between x
and y?
regression 1
$y = ax + b$
$a = 9.1$
$b = 11.8$
$r = 0.2804$
regression 2
$y = ax + b$
$a = -18.5$
$b = -1.2$
$r = -0.8314$
regression 3
$y = ax + b$
$a = 3.4$
$b = 12.9$
$r = 0.5692$
regression 4
$y = ax + b$
$a = -6$
$b = 0.3$
$r = -0.5086$
answer
regression 1
regression 3
regression 2
regression 4

Explanation:

Step1: Understand the correlation coefficient \(r\)

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

Step2: Analyze each regression

• Regression 1: \(r = 0.2804\) (positive but not close to \(1\))
• Regression 2: \(r=- 0.8314\) (negative, so not a positive relationship)
• Regression 3: \(r = 0.5692\) (positive and closer to \(1\) compared to Regression 1)
• Regression 4: \(r=-0.5086\) (negative, so not a positive relationship)

Answer:

Regression 3