Question

which of the following regressions represents the strongest positive linear relationship between x and y?
regression 1
$y = ax + b$
$a = 14.7$
$b = -18.4$
$r = 0.1262$
regression 2
$y = ax + b$
$a = -19.5$
$b = 8.7$
$r = -0.7909$
regression 3
$y = ax + b$
$a = 4.7$
$b = 17$
$r = 0.741$
regression 4
$y = ax + b$
$a = -2.4$
$b = 9.3$
$r = -0.2324$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

Step1: Recall the property of correlation coefficient

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

Step2: Analyze each regression

• Regression 1: \(r = 0.1262\). The value of \(r\) is positive but \(|r|=0.1262\) is far from \(1\).
• Regression 2: \(r=- 0.7909\). This is a negative linear relationship.
• Regression 3: \(r = 0.741\). The value of \(r\) is positive and \(|r| = 0.741\) is relatively close to \(1\) among the positive - \(r\) regressions.
• Regression 4: \(r=-0.2324\). This is a negative linear relationship.

Answer:

Regression 3