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, r=0.91r = 0.91, is very close to 1, indicating a strong positive linear association between the two variables XX and YY. 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 rr 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:

  1. How is the correlation coefficient rr calculated?
  2. What does a negative correlation coefficient mean in practical terms?
  3. How can outliers affect the value of rr?
  4. What is the difference between correlation and causation?
  5. What is the interpretation of an rr 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