Math Problem Statement
Match the correlation coefficients with the scatterplots shown below. Scatterplot Correlation coefficient [\greenD{\text{Scatterplot A}}] [\maroonD{\text{Scatterplot B}}] [\goldD{\text{Scatterplot C}}] [\blueD{\text{Scatterplot D}}] [r=0.89] [r=-0.92] [r=-0.48] [r=0.67] [\greenD{\text{Scatterplot A}}] [\maroonD{\text{Scatterplot B}}] Scatterplot A. The scatterplot has horizontal axis, x, which ranges from 0 to 9, in increments of 1, and vertical axis, y, which ranges from 0 to 9, in increments of 1. 19 points fall diagonally, in a somewhat wide, loose cluster between (0, 8.1) and (8.75, 3.5). The cluster is most heavily concentrated after x = 7. Outliers exist. Outliers exist. All values estimated. [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [y] [x] Scatterplot B. The scatterplot has horizontal axis, x, which ranges from 0 to 9, in increments of 1, and vertical axis, y, which ranges from 0 to 9, in increments of 1. 19 points fall diagonally, in a very wide, loose cluster between (1.1, 8.6) and (7.1, 2.6). Outliers exist. All values estimated. [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [y] [x] [\goldD{\text{Scatterplot C}}] [\blueD{\text{Scatterplot D}}] Scatterplot C. The scatterplot has horizontal axis, x, which ranges from 0 to 9, in increments of 1, and vertical axis, y, which ranges from 0 to 9, in increments of 1. 19 points rise diagonally in a tight, narrow cluster between (0.6, 3.8) and (8.8, 9.1). Outliers exist. All values estimated. [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [y] [x] Scatterplot D. The scatterplot has horizontal axis, x, which ranges from 0 to 9, in increments of 1, and vertical axis, y, which ranges from 0 to 9, in increments of 1. 19 points rise in a very wide, loose diagonal pattern between (0.1, 1) and (8.2, 6.75). Outliers exist. All values estimated. [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [y] [x]
Solution
To match the correlation coefficients with the scatterplots, we need to assess the strength and direction of the relationships between and in each scatterplot.
Correlation Coefficients:
- : Strong positive correlation.
- : Strong negative correlation.
- : Moderate negative correlation.
- : Moderate positive correlation.
Scatterplot Analysis:
-
Scatterplot A:
- Description: A somewhat wide, loose cluster with a negative trend.
- This suggests a moderate negative correlation.
- Match: .
-
Scatterplot B:
- Description: A very wide, loose cluster with a negative trend.
- This suggests a weaker or moderate negative correlation, but wider than A.
- Match: (If considered looser and weaker than A) or a weaker negative correlation.
-
Scatterplot C:
- Description: A tight, narrow cluster with a strong positive trend.
- This suggests a strong positive correlation.
- Match: .
-
Scatterplot D:
- Description: A very wide, loose cluster with a positive trend.
- This suggests a moderate positive correlation.
- Match: .
Final Match:
- Scatterplot A:
- Scatterplot B:
- Scatterplot C:
- Scatterplot D:
Do you want any more details or have any other questions?
Here are five related questions:
- What are some examples of real-world data that might have a strong positive correlation?
- How can outliers affect the correlation coefficient?
- Why might a loose cluster suggest a weaker correlation?
- How is the correlation coefficient calculated mathematically?
- What are the limitations of using the correlation coefficient to interpret data?
Tip: When interpreting scatterplots, always consider the direction (positive or negative) and the tightness of the cluster to gauge the strength of the correlation.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Correlation Coefficient
Scatterplots
Formulas
-
Theorems
-
Suitable Grade Level
Grades 9-12