Question

which of the following regressions represents the strongest negative linear relationship between x and y? regression 1 y = ax + b a = -9 b = -6 r = -0.4563 regression 2 y = ax + b a = 13.8 b = -8.5 r = 0.3374 regression 3 y = ax + b a = 15.2 b = -12.8 r = 0.8255 regression 4 y = ax + b a = -5.2 b = -15.2 r = -0.7049 answer regression 1 regression 3 regression 2 regression 4

Explanation:

Step1: Recall correlation - coefficient concept

The correlation - coefficient \(r\) measures the strength and direction of a linear relationship. For a negative linear relationship, the closer \(|r|\) is to 1, the stronger the negative linear relationship.

Step2: Analyze each regression's \(r\) value

Regression 1 has \(r=-0.4563\), Regression 2 has \(r = 0.3374\) (a positive relationship, so it can be excluded), Regression 3 has \(r = 0.8255\) (a positive relationship, so it can be excluded), and Regression 4 has \(r=-0.7049\).

Step3: Compare negative \(r\) values

Since \(|-0.7049|>|-0.4563|\), Regression 4 has the strongest negative linear relationship.

Answer:

Regression 4