Question

question
which of the following regressions represents the strongest negative linear relationship
between x and y?
regression 1
$y = ax + b$
$a = - 6.3$
$b = 19$
$r = - 0.7804$
regression 2
$y = ax + b$
$a = 8.6$
$b = 7.7$
$r = 0.5246$
regression 3
$y = ax + b$
$a = 15.6$
$b = - 3.1$
$r = 0.9505$
regression 4
$y = ax + b$
$a = - 14.7$
$b = - 4.7$
$r = - 0.0943$
answer
regression 1
regression 2
regression 3
regression 4
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Explanation:

Step1: Understand the 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. A negative \( r \) indicates a negative linear relationship.

Step2: Compare the absolute values of \( r \) for each regression

• For Regression 1: \( |r|=|- 0.7804| = 0.7804 \)
• For Regression 2: \( |r|=|0.5246| = 0.5246 \)
• For Regression 3: \( |r|=|0.9505| = 0.9505 \) (positive, so not a negative relationship)
• For Regression 4: \( |r|=|-0.0943| = 0.0943 \)

Since we want the strongest negative linear relationship, we look for the negative \( r \) with the largest absolute value. Among the negative \( r \) values (\( r=-0.7804\) for Regression 1 and \( r = - 0.0943\) for Regression 4), \( |-0.7804|>|-0.0943|\)

Answer:

Regression 1