Question

match each correlation coefficient to the appropriate scatter plot.
r = 0.4, r = 0.9, r = -0.4, r = -0.9 (and four scatter plots below these coefficients)

Explanation:

Step1: Recall Correlation Coefficient Rules

Correlation coefficient \( r \) ranges from \(-1\) to \(1\). Positive \( r \) means positive linear association (as \( x \) increases, \( y \) tends to increase), negative \( r \) means negative linear association (as \( x \) increases, \( y \) tends to decrease). Closer \( |r| \) is to \(1\), stronger the linear relationship; \( r = 0 \) means no linear association.

Step2: Analyze \( r = 0.0 \)

For \( r = 0.0 \), there should be no linear trend. The scatter plot with points randomly scattered (no upward/downward trend) matches. Let's check the four plots:

• Top - Left: Points seem to have no clear linear trend (scattered randomly) → candidate for \( r = 0.0 \).
• Top - Right: Points show a positive upward trend (as \( x \) increases, \( y \) increases) → positive \( r \).
• Bottom - Left: Points show a negative downward trend (as \( x \) increases, \( y \) decreases) → negative \( r \).
• Bottom - Right: Points have some scatter but maybe weak trend? Wait, Top - Left has more random scatter.

Step3: Analyze \( r = 0.9 \)

\( r = 0.9 \) is a strong positive correlation. The scatter plot with points closely following an upward - sloping line. Top - Right plot: points are close to a line with positive slope → strong positive, so \( r = 0.9 \) matches Top - Right.

Step4: Analyze \( r = - 0.9 \)

\( r=-0.9 \) is a strong negative correlation. Points closely follow a downward - sloping line. Bottom - Left plot: points are close to a line with negative slope → strong negative, so \( r = - 0.9 \) matches Bottom - Left.

Step5: Analyze \( r = 0.4 \)

\( r = 0.4 \) is a moderate positive correlation. Points show a positive trend but more scattered than \( r = 0.9 \). Bottom - Right plot: has a positive trend (as \( x \) increases, \( y \) has a general upward trend but more scattered) → moderate positive, so \( r = 0.4 \) matches Bottom - Right. And the remaining (Top - Left) is \( r = 0.0 \).

Answer:

• \( r = 0.0 \): Top - Left Scatter Plot
• \( r = 0.9 \): Top - Right Scatter Plot
• \( r=-0.9 \): Bottom - Left Scatter Plot
• \( r = 0.4 \): Bottom - Right Scatter Plot
• \( r=-0.4 \): Wait, original coefficients are \( r = 0.4,r = 0.9,r=-0.4,r = 0.0 \)? Wait, the blue boxes: \( r = 0.4 \), \( r = 0.9 \), \( r=-0.4 \), \( r = 0.0 \). So correcting Step4 and Step5:

For \( r=-0.4 \) (moderate negative), Bottom - Left? No, \( r=-0.9 \) is strong negative. Wait, my mistake earlier: the coefficients are \( r = 0.4 \), \( r = 0.9 \), \( r=-0.4 \), \( r = 0.0 \). So:

• \( r = 0.0 \): Top - Left (no trend)
• \( r = 0.9 \): Top - Right (strong positive)
• \( r=-0.4 \): Bottom - Left (moderate negative, points have negative trend but more scattered than \( r=-0.9 \), but since \( r=-0.9 \) is not in the list, the given \( r=-0.4 \) for Bottom - Left? Wait, the given coefficients are \( r = 0.4 \), \( r = 0.9 \), \( r=-0.4 \), \( r = 0.0 \). So:

Top - Left: \( r = 0.0 \) (no linear trend)
Top - Right: \( r = 0.9 \) (strong positive)
Bottom - Left: \( r=-0.4 \) (moderate negative, since \( r=-0.9 \) is not an option here? Wait, the problem has \( r=-0.4 \) not \( r=-0.9 \). So correcting:

• \( r = 0.0 \): Top - Left (random scatter)
• \( r = 0.9 \): Top - Right (strong positive, close points)
• \( r=-0.4 \): Bottom - Left (moderate negative, points with negative trend, more scattered)
• \( r = 0.4 \): Bottom - Right (moderate positive, points with positive trend, more scattered than \( r = 0.9 \))

So the matches are:
\( r = 0.0 \) → Top - Left Scatter Plot
\( r = 0.9 \) → Top - Right Scatter Plot
\( r=-0.4 \) → Bottom - Left Scatter Plot
\( r = 0.4 \) → Bottom - Right Scatter Plot