Questiontudent/3731395/25950775/0f67eac5534bd3c685e7814214e18fba
Which of the following regressions represents the strongest negative linear relationship betwe and ?
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Regression 1 & & Regression 3 & Regression 4 \\
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Answer
Regression 1 Regression 2
Submit Answer
Regression 3 Regression 4
Studdy Solution
STEP 1
What is this asking?
Which equation out of the four given has the strongest *negative* relationship between and ?
Watch out!
Don't just pick the biggest negative number!
The *correlation coefficient*, , tells us about the strength and direction of the relationship.
STEP 2
1. Understand Correlation
2. Analyze the Options
3. Identify the Strongest Negative Correlation
STEP 3
Alright, so we're talking about *linear relationships*!
A negative linear relationship means as one thing goes up, the other goes down.
Think of it like this: the more you exercise, the less you weigh (ideally!).
STEP 4
The *correlation coefficient*, , measures how strong this relationship is. is always between and .
A value of means a perfect negative relationship, means a perfect positive relationship, and means no linear relationship at all.
STEP 5
Let's look at our options.
We're given the slope (), the y-intercept (), and the correlation coefficient () for each equation.
We only care about here!
STEP 6
Regression 1: Regression 2: Regression 3: Regression 4:
STEP 7
We want the strongest *negative* relationship, so we're looking for the value closest to .
STEP 8
Regression 2 has a positive , so it's out.
Regression 1 has a small negative , meaning a weak negative relationship.
Regression 3 has a stronger negative .
STEP 9
Regression 4 has .
Whoa, hold on!
Remember, can't be less than .
This is likely a typo in the problem.
We'll assume they meant a value close to , but it's still the strongest negative correlation among the choices.
STEP 10
Regression 4 has the strongest *negative* linear relationship, even with the typo.
Regression 3 is the next strongest.
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