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 xx and yy in each scatterplot.

Correlation Coefficients:

  • r=0.89r = 0.89: Strong positive correlation.
  • r=0.92r = -0.92: Strong negative correlation.
  • r=0.48r = -0.48: Moderate negative correlation.
  • r=0.67r = 0.67: Moderate positive correlation.

Scatterplot Analysis:

  1. Scatterplot A:

    • Description: A somewhat wide, loose cluster with a negative trend.
    • This suggests a moderate negative correlation.
    • Match: r=0.48r = -0.48.
  2. 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: r=0.48r = -0.48 (If considered looser and weaker than A) or a weaker negative correlation.
  3. Scatterplot C:

    • Description: A tight, narrow cluster with a strong positive trend.
    • This suggests a strong positive correlation.
    • Match: r=0.89r = 0.89.
  4. Scatterplot D:

    • Description: A very wide, loose cluster with a positive trend.
    • This suggests a moderate positive correlation.
    • Match: r=0.67r = 0.67.

Final Match:

  • Scatterplot A: r=0.48r = -0.48
  • Scatterplot B: r=0.92r = -0.92
  • Scatterplot C: r=0.89r = 0.89
  • Scatterplot D: r=0.67r = 0.67

Do you want any more details or have any other questions?

Here are five related questions:

  1. What are some examples of real-world data that might have a strong positive correlation?
  2. How can outliers affect the correlation coefficient?
  3. Why might a loose cluster suggest a weaker correlation?
  4. How is the correlation coefficient calculated mathematically?
  5. 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.

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Math Problem Analysis

Mathematical Concepts

Correlation Coefficient
Scatterplots

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12