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 = -3.8 b = -7.3 r = -0.8516 regression 2 y = ax + b a = 19.7 b = 13.2 r = 0.1204 regression 3 y = ax + b a = -10 b = -6.1 r = -0.8836 regression 4 y = ax + b a = 1.8 b = 4.6 r = 0.3766 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 = -3.8 b = -7.3 r = -0.8516 regression 2 y = ax + b a = 19.7 b = 13.2 r = 0.1204 regression 3 y = ax + b a = -10 b = -6.1 r = -0.8836 regression 4 y = ax + b a = 1.8 b = 4.6 r = 0.3766 answer regression 1 regression 2 regression 3 regression 4

Answer

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|=|- 0.8516| = 0.8516). For Regression 2: (|r_2|=|0.1204| = 0.1204). For Regression 3: (|r_3|=|-0.8836| = 0.8836). For Regression 4: (|r_4|=|0.3766| = 0.3766).

Step3: Compare absolute - values

We compare (0.8516), (0.1204), (0.8836), and (0.3766). We find that (0.1204) is the smallest among them.

Answer:

Regression 2