Question

which of the following regressions represents the strongest negative linear relationship between x and y?

regression 1
$y = ax + b$
$a = -15$
$b = -18.2$
$r = -0.1439$

regression 2
$y = ax + b$
$a = -6.5$
$b = -0.3$
$r = -0.7514$

regression 3
$y = ax + b$
$a = 16.9$
$b = -12.4$
$r = 0.7737$

regression 4
$y = ax + b$
$a = -5.3$
$b = -13.6$
$r = -1.0863$

answer
\bigcirc regression 1 \bigcirc regression 2
\bigcirc regression 3 \bigcirc regression 4
submit answer

Explanation:

Step1: Recall correlation rules

The correlation coefficient $r$ must satisfy $-1 \leq r \leq 1$. Values outside this range are invalid.

Step2: Filter valid negative $r$ values

• Regression 1: $r=-0.1439$ (valid, negative)
• Regression 2: $r=-0.7514$ (valid, negative)
• Regression 3: $r=0.7737$ (positive, discard)
• Regression 4: $r=-1.0863$ (invalid, discard)

Step3: Compare strength of negative $r$

Strongest negative relationship corresponds to the $r$ value closest to $-1$.
$\vert -0.7514 \vert > \vert -0.1439 \vert$

Answer:

Regression 2