Math Problem Statement

Match these values of r (-0.997, -1, 0.997, -0.361, and 0.696) with their corresponding scatterplots.

Solution

From the images you have uploaded, I can provide guidance on matching the values of rr (correlation coefficients) with the scatterplots. Here's how to interpret each rr value:

  1. r=1r = -1: Perfect negative correlation; points form a straight line with a downward slope.
  2. r=0.997r = -0.997: Strong negative correlation; points are very close to a straight line with a downward slope but may have slight deviation.
  3. r=0.361r = -0.361: Weak negative correlation; points are somewhat scattered but still trend downward.
  4. r=0.696r = 0.696: Moderate positive correlation; points form a trend upward, but there is noticeable scatter.
  5. r=0.997r = 0.997: Strong positive correlation; points are close to a straight line with an upward slope.

Observing Scatterplots:

  • Scatterplot 3 appears to show a nearly perfect straight line trending downward, which corresponds to r=1r = -1.
  • Scatterplot 1 has a strong negative trend but with slight scatter, corresponding to r=0.997r = -0.997.
  • Scatterplot 4 shows a weak negative trend with significant scatter, corresponding to r=0.361r = -0.361.
  • Scatterplot 5 shows a strong positive trend, corresponding to r=0.997r = 0.997.
  • Scatterplot 2 has a moderate positive trend with noticeable scatter, corresponding to r=0.696r = 0.696.

Assigning rr Values:

  1. Scatterplot 1: r=0.997r = -0.997
  2. Scatterplot 2: r=0.696r = 0.696
  3. Scatterplot 3: r=1r = -1
  4. Scatterplot 4: r=0.361r = -0.361
  5. Scatterplot 5: r=0.997r = 0.997

Let me know if you have further questions or need additional explanations!


Relative Questions:

  1. What does the magnitude of rr indicate about the strength of correlation?
  2. How would you describe the difference between r=0.361r = -0.361 and r=0.696r = 0.696?
  3. Why is it important to visually confirm a correlation even when the rr value is provided?
  4. How can outliers affect the calculation of rr and the visual scatterplot?
  5. What real-life data might exhibit a strong negative or positive correlation like r=0.997r = 0.997 or r=1r = -1?

Tip: Always examine scatterplots alongside their correlation coefficient rr; even high values of rr might not always reflect linearity if outliers dominate

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient (r)
Linear Relationships
Scatterplots

Formulas

r = Σ[(x - x̄)(y - ȳ)] / √[Σ(x - x̄)^2 * Σ(y - ȳ)^2]

Theorems

Pearson Correlation Coefficient

Suitable Grade Level

Grades 9-12