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 rr is 0.498-0.498, accurate to three decimal places.

The proportion of the variation in yy that can be explained by the variation in the values of xx (denoted R2R^2) is approximately 24.8%24.8\%.

Do you have any further questions or would you like more details?

Here are five related questions to expand this topic:

  1. How do we interpret a negative correlation coefficient?
  2. What does an R2R^2 value of 24.8% indicate about the strength of the relationship?
  3. How can we compute the slope and intercept of the regression line for this data?
  4. What methods can we use to visually represent the relationship between xx and yy?
  5. How does the value of R2R^2 change if outliers are removed?

Tip: When interpreting R2R^2, 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)