Question

r = 0.4
r = 0.9
r = -0.4
r = -1
smartscore
out of 100
time
elapsed
01
07
%

Explanation:

To solve the problem of matching the scatter plots with their corresponding correlation coefficients (\( r \)), we analyze the direction and strength of the linear relationship in each plot:

1. Understanding Correlation Coefficients:

• \( r = 1 \) or \( r = -1 \): Perfect linear relationship (all points lie on a straight line).
• \( |r| \) close to 1: Strong linear relationship (points cluster tightly around a line).
• \( |r| \) close to 0: Weak linear relationship (points are scattered with little linear trend).
• Positive \( r \): As \( x \) increases, \( y \) tends to increase (upward trend).
• Negative \( r \): As \( x \) increases, \( y \) tends to decrease (downward trend).

2. Analyzing Each Plot:

Plot with \( r = -1 \):

• This plot shows a perfect negative linear relationship (all points lie on a straight line with a negative slope). As \( x \) increases, \( y \) decreases in a perfectly linear fashion.

Plot with \( r = 0.9 \):

• This plot shows a strong positive linear relationship (points cluster tightly around an upward - sloping line). The high \( |r| \) (0.9) indicates a strong linear trend.

Plot with \( r = -0.4 \):

• This plot shows a weak negative linear relationship (points are scattered but show a slight downward trend as \( x \) increases). The \( |r| = 0.4 \) (close to 0) indicates a weak trend, and the negative sign indicates a downward slope.

Plot with \( r = 0.4 \):

• This plot shows a weak positive linear relationship (points are scattered but show a slight upward trend as \( x \) increases). The \( |r| = 0.4 \) (close to 0) indicates a weak trend, and the positive sign indicates an upward slope.

3. Matching Plots to \( r \):

• Perfect negative linear relationship (all points on a line, downward slope) → \( r = -1 \).
• Strong positive linear relationship (points tightly clustered, upward slope) → \( r = 0.9 \).
• Weak negative linear relationship (scattered points, slight downward slope) → \( r = -0.4 \).
• Weak positive linear relationship (scattered points, slight upward slope) → \( r = 0.4 \).

Final Matches:

• Plot with perfect negative line: \( r = -1 \)
• Plot with strong positive cluster: \( r = 0.9 \)
• Plot with weak negative scatter: \( r = -0.4 \)
• Plot with weak positive scatter: \( r = 0.4 \)

(Note: If the task is to label a specific plot, identify its trend/strength and match to the corresponding \( r \). For example, the plot with the perfect negative line is \( r = -1 \), the strong positive cluster is \( r = 0.9 \), etc.)

Answer:

To solve the problem of matching the scatter plots with their corresponding correlation coefficients (\( r \)), we analyze the direction and strength of the linear relationship in each plot:

1. Understanding Correlation Coefficients:

• \( r = 1 \) or \( r = -1 \): Perfect linear relationship (all points lie on a straight line).
• \( |r| \) close to 1: Strong linear relationship (points cluster tightly around a line).
• \( |r| \) close to 0: Weak linear relationship (points are scattered with little linear trend).
• Positive \( r \): As \( x \) increases, \( y \) tends to increase (upward trend).
• Negative \( r \): As \( x \) increases, \( y \) tends to decrease (downward trend).

2. Analyzing Each Plot:

Plot with \( r = -1 \):

• This plot shows a perfect negative linear relationship (all points lie on a straight line with a negative slope). As \( x \) increases, \( y \) decreases in a perfectly linear fashion.

Plot with \( r = 0.9 \):

• This plot shows a strong positive linear relationship (points cluster tightly around an upward - sloping line). The high \( |r| \) (0.9) indicates a strong linear trend.

Plot with \( r = -0.4 \):

• This plot shows a weak negative linear relationship (points are scattered but show a slight downward trend as \( x \) increases). The \( |r| = 0.4 \) (close to 0) indicates a weak trend, and the negative sign indicates a downward slope.

Plot with \( r = 0.4 \):

• This plot shows a weak positive linear relationship (points are scattered but show a slight upward trend as \( x \) increases). The \( |r| = 0.4 \) (close to 0) indicates a weak trend, and the positive sign indicates an upward slope.

3. Matching Plots to \( r \):

• Perfect negative linear relationship (all points on a line, downward slope) → \( r = -1 \).
• Strong positive linear relationship (points tightly clustered, upward slope) → \( r = 0.9 \).
• Weak negative linear relationship (scattered points, slight downward slope) → \( r = -0.4 \).
• Weak positive linear relationship (scattered points, slight upward slope) → \( r = 0.4 \).

Final Matches:

• Plot with perfect negative line: \( r = -1 \)
• Plot with strong positive cluster: \( r = 0.9 \)
• Plot with weak negative scatter: \( r = -0.4 \)
• Plot with weak positive scatter: \( r = 0.4 \)

(Note: If the task is to label a specific plot, identify its trend/strength and match to the corresponding \( r \). For example, the plot with the perfect negative line is \( r = -1 \), the strong positive cluster is \( r = 0.9 \), etc.)