Question

question
which of the following regressions represents the weakest linear relationship between x
and y?
regression 1
$y = ax + b$
$a = - 16$
$b = 2.2$
$r = - 0.6913$
regression 2
$y = ax + b$
$a = - 12.1$
$b = 19.1$
$r = - 0.6559$
regression 3
$y = ax + b$
$a = 10.1$
$b = - 3.8$
$r = 0.212$
regression 4
$y = ax + b$
$a = - 6.4$
$b = 10.6$
$r = - 0.8424$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \( r \) measures the strength of a linear relationship. The closer \( |r| \) is to \( 1 \), the stronger the linear relationship. The closer \( |r| \) is to \( 0 \), the weaker the linear relationship.

Step2: Compare the absolute values of \( r \)

For Regression 1: \( |r|=|- 0.6913| = 0.6913 \)
For Regression 2: \( |r|=|-0.6559| = 0.6559 \)
For Regression 3: \( |r|=|0.212| = 0.212 \)
For Regression 4: \( |r|=|-0.8424| = 0.8424 \)

Since \( 0.212<0.6559 < 0.6913<0.8424 \), Regression 3 has the smallest \( |r| \) value.

Answer:

Regression 3