Math Problem Statement
Solution
To find the correlation coefficient for the data in the table, we can use a statistical calculator or software to calculate the correlation coefficient (denoted as ) for the pairs of weight () and height () values.
The data pairs are:
- (Weight): 8, 12, 18, 24, 30, 32, 35, 37, 40
- (Height): 22, 23, 26, 30, 32, 33, 35, 36, 38
Steps to Calculate the Correlation Coefficient :
- Compute the mean of values and the mean of values.
- Calculate the deviation of each and value from their respective means.
- Find the product of these deviations for each data pair.
- Calculate the square of each deviation for both and .
- Use the correlation formula:
After using technology or calculator to compute this, we get a correlation coefficient .
Thus, the correct answer is:
- 0.997
Would you like a detailed breakdown of these calculations?
Further Questions
- What does a correlation coefficient close to 1 imply about the relationship between weight and height in this data?
- How would you interpret a correlation coefficient of -0.503 in a similar context?
- Can you identify any outliers in this data set based on the correlation coefficient?
- How would the correlation coefficient change if there were an error in one of the data points?
- Why is it important to verify the assumptions of linearity before relying on the correlation coefficient?
Tip
Always interpret correlation in the context of the data. A high correlation does not imply causation but indicates a strong association between variables.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Linear Relationships
Formulas
Correlation coefficient formula: r = (Σ(x - x̄)(y - ȳ)) / √(Σ(x - x̄)^2 * Σ(y - ȳ)^2)
Theorems
Pearson Correlation Coefficient
Suitable Grade Level
Grades 10-12
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