Question

which of the following regressions represents the weakest linear relationship between x and y?
regression 1
$y = ax + b$
$a = 14.6$
$b = 14.3$
$r = 0.1906$
regression 2
$y = ax + b$
$a = 5.6$
$b = 8$
$r = 0.6215$
regression 3
$y = ax + b$
$a = 5.2$
$b = 1.3$
$r = 0.1853$
regression 4
$y = ax + b$
$a = 5.3$
$b = -5.5$
$r = 0.4701$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

Step1: Recall the concept of correlation coefficient

The correlation coefficient \(r\) measures the strength of a linear relationship. The closer \(|r|\) is to \(0\), the weaker the linear relationship.

Step2: Compare the absolute values of \(r\) for each regression

For Regression 1: \(|r| = |0.1906|=0.1906\)
For Regression 2: \(|r| = |0.6215| = 0.6215\)
For Regression 3: \(|r|=|0.1853| = 0.1853\)
For Regression 4: \(|r|=|0.4701|=0.4701\)

Since \(0.1853<0.1906 < 0.4701<0.6215\)

Answer:

Regression 3