Question

question
which of the following regressions represents the strongest linear relationship between
x and y?
regression 1
y = ax + b
a = -13.4
b = -5.8
r = -1.1915
regression 2
y = ax + b
a = 3.3
b = 11.4
r = 0.8621
regression 3
y = ax + b
a = 1.6
b = -13.4
r = 0.3816
regression 4
y = ax + b
a = -17.3
b = 7.3
r = -0.6936
answer
regression 1
regression 2
regression 3
regression 4
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Explanation:

Step1: Recall the concept of correlation coefficient

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

Step2: Compare the magnitudes of \( r \) values

For Regression 1: \( |r|=|- 1.1915| = 1.1915\) (but \(|r|\leq1\), this is an error, likely a typo. Assuming it's a wrong entry).
For Regression 2: \( |r| = |0.8621|=0.8621 \).
For Regression 3: \( |r|=|0.3816| = 0.3816\).
For Regression 4: \( |r|=|-0.6936|=0.6936\).

Since \(0.8621>0.6936 > 0.3816\) (ignoring the impossible \(|r| = 1.1915\) value for Regression 1 as it violates \(|r|\leq1\) rule).

Answer:

Regression 2