Question

which of the following regressions represents the weakest linear relationship between x and y? regression 1 y = ax + b a = 6.5 b = 5.8 r = 0.5476 regression 2 y = ax + b a = -11.8 b = -4.7 r = -0.5976 regression 3 y = ax + b a = -15 b = 5.5 r = -0.3574 regression 4 y = ax + b a = -4 b = 13 r = -0.2755 regression 2 regression 4

Explanation:

Step1: Recall correlation - coefficient concept

The absolute - value of the correlation coefficient \(r\) measures the strength of the linear relationship. A value of \(|r|\) close to 0 indicates a weak linear relationship, and a value of \(|r|\) close to 1 indicates a strong linear relationship.

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

For Regression 1: \(|r_1|=|0.5476|\)
For Regression 2: \(|r_2| = |- 0.5976|=0.5976\)
For Regression 3: \(|r_3|=|-0.3574| = 0.3574\)
For Regression 4: \(|r_4|=|-0.2755|=0.2755\)

Step3: Compare absolute - values

We have \(|r_1| = 0.5476\), \(|r_2|=0.5976\), \(|r_3| = 0.3574\), \(|r_4|=0.2755\). Since \(0.2755<0.3574<0.5476<0.5976\), Regression 4 has the smallest absolute - value of the correlation coefficient.

Answer:

Regression 4