which of the following regressions represents the weakest linear relationship between x and y? regression 1…

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 2 regression 3 regression 4

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 2 regression 3 regression 4

Answer

Explanation:

Step1: Recall correlation - coefficient concept

The absolute - value of the correlation coefficient (r) measures the strength of the linear relationship. 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 (0.1967), (0.2444), (0.3614), and (0.5936). Since (0.1967) is the smallest, Regression 4 has the weakest linear relationship.

Answer:

Regression 4