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=0.65] [r=0.84] [r=-0.02] [r=-0.72] [\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 in a very wide diagonal pattern between (1.1, 5.7) and (8.3, 0). 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 rise diagonally in a tight narrow cluster between (0.1, 4.1) and (8.75, 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]

Solution

To match the correlation coefficients rr with the scatterplots, we need to evaluate how closely the points fit a line and whether the trend is positive, negative, or neutral. Here's how we can analyze the scatterplots based on their descriptions:

  1. Scatterplot A:

    • The points fall in a wide diagonal pattern from approximately (1.1, 5.7) to (8.3, 0), indicating a negative trend.
    • The points are spread out, not tightly clustered, but there is a clear negative direction.
    • This suggests a moderately negative correlation.
    • Best match: r=−0.72r = -0.72 (moderate negative correlation).

  2. Scatterplot B:

    • The points rise diagonally in a tight narrow cluster from approximately (0.1, 4.1) to (8.75, 9.1), indicating a strong positive trend.
    • The tight clustering suggests a strong positive correlation.
    • Best match: r=0.84r = 0.84 (strong positive correlation).

Remaining Scatterplots and Correlations:

Without the descriptions of the remaining scatterplots C and D, we would assign the remaining correlation coefficients based on general scatterplot patterns:

  • r=0.65r = 0.65 likely corresponds to a moderate positive trend.
  • r=−0.02r = -0.02 would correspond to a random scatter with almost no correlation.

Would you like details on how to match the rest?

Related Questions:

  1. What is the difference between a strong and weak correlation?
  2. How do positive and negative correlations affect data interpretation?
  3. Can a scatterplot have outliers and still show a strong correlation?
  4. What does a correlation of r=0r = 0 signify?
  5. How is the correlation coefficient rr calculated from data points?

Tip:

Correlation does not imply causation—always be cautious when interpreting relationships between variables.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Scatterplots

Formulas

Correlation coefficient formula r = (Σ(xy) - (Σx)(Σy)/n) / (sqrt[Σx² - (Σx)²/n] * sqrt[Σy² - (Σy)²/n])

Theorems

Pearson correlation theorem

Suitable Grade Level

Grades 10-12

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