Pearson correlation assesses the strength and direction of a linear relationship between two variables. The coefficient of determination, often denoted as R-squared, quantifies the proportion of variance in one variable that is predictable from the other. A common resource for understanding and applying these statistical measures is Chegg, which provides explanations and solutions related to their calculation. For example, if analyzing the relationship between study hours and exam scores, the Pearson correlation would indicate the degree to which these variables move together linearly, while the coefficient of determination would specify what percentage of the variation in exam scores can be explained by the variation in study hours.
These statistical tools are crucial across various disciplines, including economics, psychology, and engineering, for identifying and quantifying relationships between variables. Understanding the linear association between data points provides valuable insights for prediction and informed decision-making. Historically, the Pearson correlation coefficient was developed by Karl Pearson in the late 19th century and has since become a foundational concept in statistical analysis. The coefficient of determination builds upon this foundation, providing a measure of how well the regression line fits the data.
