Math Problem Statement
Solution
The scatter plot shows a negative trend, where the values of decrease as 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 decreases as 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:
- How is the correlation coefficient calculated mathematically?
- What does a perfect correlation coefficient of -1 represent?
- Can a correlation coefficient determine causation between two variables?
- What factors could reduce the strength of a correlation in a dataset?
- 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