Question

which of the following regressions represents the weakest linear relationship between x and y? regression 1 y = ax + b a = 3.3 b = 13.1 r = 0.3614 regression 2 y = ax + b a = -15.9 b = -12.3 r = -0.2444 regression 3 y = ax + b a = -15.5 b = -8.9 r = -0.5936 regression 4 y = ax + b a = -15.8 b = 10.8 r = -0.1967 answer regression 1 regression 3 regression 2 regression 4

Explanation:

Step1: Recall correlation - coefficient concept

The strength of a linear relationship is determined by the absolute - value of the correlation coefficient \(r\). The closer \(|r|\) is to 0, the weaker the linear relationship.

Step2: Calculate absolute - values of \(r\) for each regression

For Regression 1: \(|r_1|=|0.3614| = 0.3614\).
For Regression 2: \(|r_2|=|- 0.2444|=0.2444\).
For Regression 3: \(|r_3|=|-0.5936| = 0.5936\).
For Regression 4: \(|r_4|=|-0.1967|=0.1967\).

Step3: Compare absolute - values

We compare the values \(0.3614\), \(0.2444\), \(0.5936\), and \(0.1967\).
Since \(0.1967<0.2444<0.3614<0.5936\), Regression 4 has the weakest linear relationship.

Answer:

Regression 4