Math Problem Statement

What is the best estimate of the correlation coefficient for the data set shown in the scatter plot?

Solution

The scatter plot shows a negative trend, where the values of yy decrease as xx increases. The points are tightly clustered along a linear trend, indicating a strong negative correlation.

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation). Based on the plot:

  • The correlation is negative because yy decreases as xx increases.
  • The strong clustering around the line suggests a correlation close to -1.

Thus, the best estimate of the correlation coefficient is A. -0.9.

Would you like further explanation or analysis on this?

Here are five follow-up questions for deeper understanding:

  1. How is the correlation coefficient calculated mathematically?
  2. What does a perfect correlation coefficient of -1 represent?
  3. Can a correlation coefficient determine causation between two variables?
  4. What factors could reduce the strength of a correlation in a dataset?
  5. How would this graph differ if the correlation coefficient were close to 0?

Tip: Always analyze the scatter plot's trend direction and point clustering to estimate the correlation coefficient effectively.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient
Scatter Plot Analysis

Formulas

Correlation coefficient formula (r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)²Σ(y - ȳ)²))

Theorems

Properties of Correlation Coefficients

Suitable Grade Level

Grades 8-10