Question

question: which of the following regressions represents the strongest positive linear relationship between x and y? regression 1: y = ax + b, a = 11.6, b = 1.8, r = 0.2697; regression 2: y = ax + b, a = 3, b = - 4.9, r = 1.0704; regression 3: y = ax + b, a = - 17.5, b = - 19.9, r = - 0.8301; regression 4: y = ax + b, a = 2.3, b = 8.6, r = 0.8193. answer: regression 1, regression 2, regression 3, regression 4

Explanation:

Step1: Recall correlation - coefficient concept

The correlation - coefficient $r$ measures the strength and direction of a linear relationship. The value of $r$ ranges from - 1 to 1. A positive linear relationship has $r>0$, and the closer $r$ is to 1, the stronger the positive linear relationship.

Step2: Analyze each regression's $r$ value

For Regression 1, $r = 0.2697$.
For Regression 2, $r = 1.0704$ which is not valid as $-1\leq r\leq1$.
For Regression 3, $r=-0.8301$ which represents a negative linear relationship.
For Regression 4, $r = 0.8193$.

Answer:

Regression 4