Math  /  Data & Statistics

QuestionWhich of the following regressions represents the strongest negative linear relationship between x and y?y ? \begin{tabular}{llll} Regression 1 &  Regression 2 \underline{\text { Regression 2 }} & Regression3 &  Regression 4 \underline{\text { Regression 4 }} \\ \begin{tabular}{ll} y=ax+by=a x+b & y=ax+by=a x+b \end{tabular} & y=ax+by=a x+b & y=ax+by=a x+b \\ a=13.9a=-13.9 & a=16.6a=16.6 & a=6a=-6 & a=8.3a=-8.3 \\ b=17b=-17 & b=7.1b=7.1 & b=4.8b=-4.8 & b=9.7b=9.7 \\ r=0.1784r=-0.1784 & r=0.7118r=0.7118 & r=0.5003r=-0.5003 & r=1.057r=-1.057 \end{tabular}
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 xx and yy? Watch out! Don't just pick the biggest negative number!
The correlation coefficient rr tells us about the strength and direction of the relationship, and it has special rules!

STEP 2

1. Understand Correlation
2. Evaluate the Options

STEP 3

The *correlation coefficient*, often represented as rr, measures how closely our data points hug a line.
It tells us two main things: *strength* and *direction*.

STEP 4

An rr value close to +1+1 or 1-1 means a super strong linear relationship!
An rr close to 00 means the points are scattered all over, like a confetti explosion, and there's no linear relationship.

STEP 5

A *positive* rr (like 0.80.8) means that as xx goes up, yy goes up too.
A *negative* rr (like 0.8-0.8) means as xx goes up, yy goes down.

STEP 6

rr *must* be between 1-1 and 11.
A value outside this range means something went wrong in the calculation!

STEP 7

r=0.1784r = -0.1784.
This is a negative relationship, but it's pretty weak.

STEP 8

r=0.7118r = 0.7118.
This is a positive relationship, so it's not what we're looking for.

STEP 9

r=0.5003r = -0.5003.
This is a negative relationship and moderately strong.
It's stronger than Regression 1!

STEP 10

r=1.057r = -1.057.
Woah there!
This value is outside the allowed range for rr.
This regression is automatically disqualified!

STEP 11

Regression 3 has the strongest *negative* linear relationship with r=0.5003r = -0.5003.

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