Math Problem Statement
Here is a bivariate data set. x y 42.1 37.1 34.1 106.2 36.3 29.4 41.1 159.6 25.5 110.1 34.7 133.1 30.5 64.3 28.2 91.3 28.3 104.5 11.6 98.1 44.2 -20 34 116.8 47.9 -33.8 This data can be downloaded as a *.csv file with this link: Download CSV
Find the correlation coefficient and report it accurate to three decimal places. r =
What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. R² = %
Solution
The correlation coefficient is , accurate to three decimal places.
The proportion of the variation in that can be explained by the variation in the values of (denoted ) is approximately .
Do you have any further questions or would you like more details?
Here are five related questions to expand this topic:
- How do we interpret a negative correlation coefficient?
- What does an value of 24.8% indicate about the strength of the relationship?
- How can we compute the slope and intercept of the regression line for this data?
- What methods can we use to visually represent the relationship between and ?
- How does the value of change if outliers are removed?
Tip: When interpreting , remember that it represents the percentage of variation in the dependent variable explained by the independent variable.
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Bivariate Data Analysis
Regression Analysis
Formulas
Correlation coefficient (r): r = Σ[(x_i - mean_x)(y_i - mean_y)] / sqrt(Σ(x_i - mean_x)^2 Σ(y_i - mean_y)^2)
Coefficient of Determination (R²): R² = r² * 100
Theorems
Pearson Correlation Coefficient
Suitable Grade Level
Undergraduate (Statistics/High School Advanced Mathematics)
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