Question

which of the following regressions represents the strongest linear relationship between x and y? regression 1 y = ax + b a = -3.2 b = -17.6 r = -1.1522 regression 2 y = ax + b a = -8.5 b = 4.9 r = -0.6431 regression 3 y = ax + b a = -7.3 b = -6.6 r = -0.8719 regression 4 y = ax + b a = 19.2 b = -6 r = 0.1839 answer regression 1 regression 2 regression 3 regression 4

Explanation:

Step1: Recall correlation - coefficient property

The strength of a linear relationship is determined by the absolute - value of the correlation coefficient $r$. The closer $|r|$ is to 1, the stronger the linear relationship.

Step2: Calculate absolute - values of $r$ for each regression

For Regression 1: $|r_1| = | - 1.1522|$. But the correlation coefficient $r$ must be in the range $[-1,1]$, so this value is incorrect.
For Regression 2: $|r_2|=| - 0.6431| = 0.6431$.
For Regression 3: $|r_3|=| - 0.8719| = 0.8719$.
For Regression 4: $|r_4|=|0.1839| = 0.1839$.

Step3: Compare absolute - values

Since $0.8719>0.6431 > 0.1839$, Regression 3 has the strongest linear relationship among the valid regressions.

Answer:

Regression 3