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 association between the two variables and . A correlation coefficient of 1 would represent a perfect positive linear relationship, while 0 would indicate no linear relationship, and -1 would represent a perfect negative linear relationship.
Since is positive and close to 1, the correct interpretation is:
D. There is a strong positive linear association between the two variables.
Would you like further details or clarifications on this? Here are 5 related questions you could explore:
- How is the correlation coefficient calculated?
- What does a negative correlation coefficient mean in practical terms?
- How can outliers affect the value of ?
- What is the difference between correlation and causation?
- What is the interpretation of an value close to 0?
Tip: Always check the sign and magnitude of the correlation coefficient. Positive values indicate a direct relationship, while negative values indicate an inverse one.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation Coefficient
Formulas
Correlation coefficient formula: r = Σ[(X_i - X̄)(Y_i - Ȳ)] / sqrt[Σ(X_i - X̄)^2 Σ(Y_i - Ȳ)^2]
Theorems
Pearson Correlation Theorem
Suitable Grade Level
Grades 10-12
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