Math Problem Statement

Match these values of r with the accompanying​ scatterplots: 0.705​, 0.331​, −0.331​, 1​, and −1. Scatterplot 1 Scatterplot 2 Scatterplot 3 0 0.2 0.4 0.6 0.8 1 10 11 12 13 14 15 x y

A scatterplot has a horizontal x-axis labeled from 0 to 1 in increments of 0.1 and a vertical y-axis labeled from 10 to 15 in increments of 1. Ten points strictly follow the pattern of a line that rises from left to right through the points (0.09, 10.45) and (0.95, 14.75). All coordinates are approximate. 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 x y

A scatterplot has a horizontal x-axis labeled from 0 to 1 in increments of 0.1 and a vertical y-axis labeled from 0 to 8 in increments of 1. Ten points with varying vertical spread very loosely follow the pattern of a line that rises from left to right through the approximate points (0,4) and (1,5). 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 x y

A scatterplot has a horizontal x-axis labeled from 0 to 1 in increments of 0.1 and a vertical y-axis labeled from 0 to 8 in increments of 1. Ten points with varying vertical spread very loosely follow the pattern of a line that falls from left to right through the approximate points (0,5) and (1,4). Scatterplot 4 Scatterplot 5 0 0.2 0.4 0.6 0.8 1 -4 -3 -2 -1 0 x y

A scatterplot has a horizontal x-axis labeled from 0 to 1 in increments of 0.1 and a vertical y-axis labeled from negative 4 to 0 in increments of 1. Ten points strictly follow the pattern of a line that falls from left to right through the points (0.09, negative 0.36) and (0.95, negative 3.79). All coordinates are approximate. 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 x y

A scatterplot has a horizontal x-axis labeled from 0 to 1 in increments of 0.1 and a vertical y-axis labeled from 0 to 8 in increments of 1. Ten points generally follow the pattern of a line that rises from left to right through the approximate points (0.1,1) and (0.9,7). The vertical spread of the points averages to approximately 2 units.

Match the values of r to the scatterplots. Scatterplot​ 1, requals= ▼ Scatterplot​ 2, requals= ▼ −0.331 0.705 0.331 1 −1 Scatterplot​ 3, requals= ▼ 0.705 −1 −0.331 1 0.331 Scatterplot​ 4, requals= ▼ 0.331 −1 1 0.705 −0.331 Scatterplot​ 5, requals= ▼ 0.705 −1 1 −0.331 0.331

Solution

Here’s how the values of rr (correlation coefficients) match the scatterplots based on the descriptions:

  1. Scatterplot 1, r=1r = 1:

    • Description: Points strictly follow a line rising from left to right.
    • Reasoning: A perfect positive linear relationship corresponds to r=1r = 1.

  2. Scatterplot 2, r=0.331r = 0.331:

    • Description: Points loosely follow a line rising from left to right with a small spread.
    • Reasoning: A weak positive linear relationship corresponds to a small positive rr, here r=0.331r = 0.331.

  3. Scatterplot 3, r=−0.331r = -0.331:

    • Description: Points loosely follow a line falling from left to right with a small spread.
    • Reasoning: A weak negative linear relationship corresponds to a small negative rr, here r=−0.331r = -0.331.

  4. Scatterplot 4, r=−1r = -1:

    • Description: Points strictly follow a line falling from left to right.
    • Reasoning: A perfect negative linear relationship corresponds to r=−1r = -1.

  5. Scatterplot 5, r=0.705r = 0.705:

    • Description: Points follow a moderately strong rising pattern with an average vertical spread of 2 units.
    • Reasoning: A moderately strong positive relationship corresponds to r=0.705r = 0.705.

Final Assignments:

  • Scatterplot 1: r=1r = 1
  • Scatterplot 2: r=0.331r = 0.331
  • Scatterplot 3: r=−0.331r = -0.331
  • Scatterplot 4: r=−1r = -1
  • Scatterplot 5: r=0.705r = 0.705

Let me know if you want more details or explanations!

Here are 5 related questions:

  1. How does the magnitude of rr reflect the strength of the relationship?
  2. What is the significance of the sign (+ or -) of rr?
  3. What happens when rr is close to 0?
  4. How does outlier data affect the correlation coefficient?
  5. Can correlation imply causation?

Tip: Always plot the data to visually assess the relationship before relying solely on rr.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficients
Scatterplots

Formulas

Pearson correlation coefficient formula: r = Σ((x - x̄)(y - ȳ)) / (nσxσy)

Theorems

Properties of Correlation Coefficients

Suitable Grade Level

Grades 9-12

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