Question

which of the following regressions represents the strongest negative linear relationship between x and y?
regression 1
$y = ax + b$
$a = 5.5$
$b = 6.4$
$r = 0.4727$
regression 2
$y = ax + b$
$a = - 13.6$
$b = - 3.6$
$r = - 0.0479$
regression 3
$y = ax + b$
$a = - 4.1$
$b = - 15.1$
$r = - 0.8925$
regression 4
$y = ax + b$
$a = 17.9$
$b = - 7.1$
$r = 0.9767$
answer
regression 1
regression 2
regression 3
regression 4

Explanation:

The strength of a linear relationship is determined by the absolute value of the correlation coefficient \(r\). A negative \(r\) indicates a negative linear relationship.

• Regression 1: \(r = 0.4727\) (positive, so not a negative relationship).
• Regression 2: \(|r|=|- 0.0479| = 0.0479\).
• Regression 3: \(|r|=|-0.8925| = 0.8925\).
• Regression 4: \(r = 0.9767\) (positive, so not a negative relationship).

Since \(0.8925>0.0479\) and Regression 3 has a negative \(r\) value.

Answer:

Regression 3