Math Problem Statement

What would you estimate the correlation coefficient to be?

Solution

The scatter plot shown in the image appears to display a downward trend, meaning that as one variable increases, the other variable tends to decrease. This suggests a negative correlation. The points are relatively close to forming a straight line, which indicates a strong correlation.

Steps to estimate the correlation coefficient:

  1. Identify the trend: The downward slope indicates a negative correlation.
  2. Estimate the strength of the relationship: The data points are tightly clustered, suggesting a strong correlation.
  3. Match with correlation coefficients: A strong negative correlation corresponds to a value close to -1.

Given the options provided in the image, -0.9 would be the best estimate for the correlation coefficient.

Would you like more details on how correlation coefficients are calculated or interpreted?


Follow-up Questions:

  1. What is the mathematical formula for calculating the correlation coefficient rr?
  2. How does the scatter plot change when the correlation coefficient is closer to 0?
  3. What are some real-world examples where a negative correlation is observed?
  4. How does a positive correlation differ visually from a negative one on a scatter plot?
  5. What statistical tools can be used to confirm the correlation coefficient from data?

Tip:

A strong correlation does not imply causation—it only describes the strength and direction of the relationship between two variables.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Scatter Plots

Formulas

Correlation Coefficient Formula (r)

Theorems

Pearson Correlation Coefficient

Suitable Grade Level

Grades 10-12