Math Problem Statement
Values of X and Y were recorded for an additional three weeks, and the correlation coefficient, r, for the augmented data set was found to be r = 0.91.
Which of the following statements best interprets this result? A.There is a weak positive linear association between the two variables. B.There is a weak negative linear association between the two variables. C.There is a strong negative linear association between the two variables. D.There is a strong positive linear association between the two variables.
Solution
The correlation coefficient is very close to 1, indicating a strong positive linear relationship between the variables and .
The correct interpretation is:
D. There is a strong positive linear association between the two variables.
A positive correlation coefficient means that as increases, tends to increase as well, and the value of 0.91 suggests this relationship is strong.
Would you like further details on interpreting correlation coefficients or have any other questions?
Here are five related questions to expand your understanding:
- What does a correlation coefficient of represent?
- How does a correlation of differ from ?
- What is the effect of outliers on the value of the correlation coefficient?
- How can we test the significance of the correlation coefficient?
- What is the difference between correlation and causation?
Tip: A correlation coefficient close to 1 or -1 indicates a strong linear relationship, while a value close to 0 suggests little to no linear relationship.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation Coefficient
Linear Relationships
Formulas
Correlation Coefficient Formula: r = Σ[(X - X̄)(Y - Ȳ)] / [√Σ(X - X̄)^2 * Σ(Y - Ȳ)^2]
Theorems
Pearson's Correlation Theorem
Suitable Grade Level
Grades 10-12
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