How do you calculate and interpret the coefficient of determination (R-squared) in regression analysis?

Calculating and Interpreting the Coefficient of Determination (R-squared) in Regression Analysis: The coefficient of determination, often denoted as R-squared (\(R^2\)), is a crucial statistical measure in regression analysis. It quantifies the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. Here's how to calculate and interpret \(R^2\): Calculating R-squared (\(R^2\)): 1. Understand the Components: - In regression analysis, there are two sources of variation in the dependent variable (Y): - Total Sum of Squares (SST): This represents the total variability in Y and is calculated as the sum of the squared differences between each data point and the overall mean of Y. - Residual Sum of Squares (SSE): This represents the unexplained variation or error in Y and is calculated as the sum of the squared differences between the observed Y values and the predicted Y values from the regression model. 2. Calculate \(R^2\): - \(R^2\) is calculated as the proportion of the v....