Question

which of the following regressions represents the strongest linear relationship between x and y? regression 1 y = ax + b a = 2.9 b = -14.5 r = 0.3938 regression 2 y = ax + b a = 8.7 b = -9.4 r = 1.0904 regression 3 y = ax + b a = -3.3 b = -20 r = -0.2546 regression 4 y = ax + b a = 9.6 b = 13.6 r = 0.5311

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 1, the stronger the linear relationship.

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

For Regression 1: $|r_1|=|0.3938| = 0.3938$
For Regression 2: $|r_2|=|1.0904|$. But the correlation coefficient $r$ must satisfy $- 1\leq r\leq1$, so this value is invalid.
For Regression 3: $|r_3|=|-0.2546| = 0.2546$
For Regression 4: $|r_4|=|0.5311| = 0.5311$

Step3: Compare absolute - values

Since $0.2546<0.3938<0.5311$, Regression 4 has the largest valid $|r|$ value among the valid regressions.

Answer:

Regression 4