Math Problem Statement
Based on the data shown below, calculate the correlation coefficient (rounded to three decimal places)
x y
5 15.5
6 17.1
7 18.1
8 18.8
9 18.7
10 21.7
11 18.5
12 20.2
13 21.6
14 22.9
15 23.7
16 23.3
17 23.6
18 25.8
Solution
It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, you can calculate the correlation coefficient manually or use another tool. Let me know if you'd like guidance on how to do that!
Here are some questions to deepen your understanding:
- How do you interpret a correlation coefficient in statistics?
- What are the differences between positive and negative correlations?
- Can you explain the significance of using Pearson's correlation coefficient over other types?
- How do outliers in the dataset affect the correlation coefficient?
- How can you visually check for a correlation before calculating it?
Tip: Always visualize your data first with a scatter plot to get an intuitive sense of the relationship before calculating a correlation coefficient.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Linear Regression
Formulas
Pearson's Correlation Coefficient formula: r = Σ[(x - mean_x)(y - mean_y)] / sqrt[Σ(x - mean_x)^2 * Σ(y - mean_y)^2]
Theorems
Pearson's correlation coefficient
Suitable Grade Level
Grades 10-12