Question

match each scatterplot shown below with one of the four specified correlations.
a. -0.15
b. 0.36
c. 0.77
d. -0.94

Explanation:

To solve the problem of matching each scatterplot with the appropriate correlation, we analyze the direction and strength of the linear relationship in each scatterplot:

Scatterplot 1 (Top)

• Direction: Positive (as \( x \) increases, \( y \) tends to increase).
• Strength: Moderate (the points show a somewhat loose but positive linear trend).
• Correlation: Among the options, \( 0.36 \) (option b) is a moderate positive correlation, which fits this scatterplot.

Scatterplot 2 (Middle)

• Direction: Negative (as \( x \) increases, \( y \) tends to decrease).
• Strength: Weak (the points are scattered but show a slight negative trend).
• Correlation: Among the options, \( -0.15 \) (option a) is a weak negative correlation, which fits this scatterplot.

Scatterplot 3 (Bottom)

• Direction: Positive (as \( x \) increases, \( y \) tends to increase).
• Strength: Strong (the points show a tight positive linear trend).
• Correlation: Among the options, \( 0.77 \) (option c) is a strong positive correlation, which fits this scatterplot. (Note: If there was a fourth scatterplot, \( -0.94 \) (option d) would be a strong negative correlation, but based on the three shown, we match the top to b, middle to a, and bottom to c.)

Final Matches:

• Top Scatterplot: \(\boldsymbol{\text{b. } 0.36}\)
• Middle Scatterplot: \(\boldsymbol{\text{a. } -0.15}\)
• Bottom Scatterplot: \(\boldsymbol{\text{c. } 0.77}\)

(If there’s a fourth scatterplot not fully visible, the remaining correlation \(-0.94\) (d) would match a strong negative scatterplot.)

Answer:

To solve the problem of matching each scatterplot with the appropriate correlation, we analyze the direction and strength of the linear relationship in each scatterplot:

Scatterplot 1 (Top)

• Direction: Positive (as \( x \) increases, \( y \) tends to increase).
• Strength: Moderate (the points show a somewhat loose but positive linear trend).
• Correlation: Among the options, \( 0.36 \) (option b) is a moderate positive correlation, which fits this scatterplot.

Scatterplot 2 (Middle)

• Direction: Negative (as \( x \) increases, \( y \) tends to decrease).
• Strength: Weak (the points are scattered but show a slight negative trend).
• Correlation: Among the options, \( -0.15 \) (option a) is a weak negative correlation, which fits this scatterplot.

Scatterplot 3 (Bottom)

• Direction: Positive (as \( x \) increases, \( y \) tends to increase).
• Strength: Strong (the points show a tight positive linear trend).
• Correlation: Among the options, \( 0.77 \) (option c) is a strong positive correlation, which fits this scatterplot. (Note: If there was a fourth scatterplot, \( -0.94 \) (option d) would be a strong negative correlation, but based on the three shown, we match the top to b, middle to a, and bottom to c.)

Final Matches:

• Top Scatterplot: \(\boldsymbol{\text{b. } 0.36}\)
• Middle Scatterplot: \(\boldsymbol{\text{a. } -0.15}\)
• Bottom Scatterplot: \(\boldsymbol{\text{c. } 0.77}\)

(If there’s a fourth scatterplot not fully visible, the remaining correlation \(-0.94\) (d) would match a strong negative scatterplot.)