Question

for each scatterplot below, determine if the correlation displayed is positive or negative, strong, moderate, or weak, and estimate the correlation coefficient (r).
17)
positive negative none
strong moderate weak
r = -0.95
18)
positive negative none
strong moderate weak
r = 0.8
19)
positive negative none
strong moderate weak
r = 0
mrs. morris and mr. sandler want to compare the heights (in inches) of the male students in both of their homerooms.
mrs. morris homeroom
75, 75, 71, 64, 68, 74, 64, 66, 70, 71
mr. sandlers homeroom
63, 68, 70, 63, 65, 72, 66, 73, 61, 69

1. find the mean for each homeroom.

mrs. morris: 69.8
mr. sandler: 67

1. find the five - number summary for each homeroom.

mrs. morris
min: 64
q1: 66
med: 70.5
q3: 74
max: 75
mr. sandler
min: 61
q1: 63
med: 67
q3: 70
max: 73

Explanation:

17) Scatterplot Analysis

Step1: Analyze Correlation Direction

The scatterplot (17) shows a negative trend (as depth increases, temperature decreases), so correlation is negative.

Step2: Analyze Correlation Strength

The points are tightly clustered along a line, indicating a strong negative correlation. A strong negative correlation has \( r \) close to -1, so estimate \( r \approx -0.95 \) (matches the given value).

Step1: Analyze Correlation Direction

The scatterplot (18) shows a positive trend (as age increases, height increases), so correlation is positive.

Step2: Analyze Correlation Strength

The points are somewhat clustered but not extremely tight, indicating a strong positive correlation (close to 1). Estimate \( r \approx 0.8 \) (matches the given value).

Step1: Analyze Correlation Direction

The scatterplot (19) has points with no clear upward or downward trend (randomly scattered), so correlation is none (no linear relationship).

Step2: Analyze Correlation Strength

With no trend, the strength is weak (or no correlation), so \( r \approx 0 \) (matches the given value).

Answer:

Direction: Negative, Strength: Strong, \( r = -0.95 \)

18) Scatterplot Analysis