What does R-squared tell you in regression output?

What does R-squared tell you in regression output?

• A. The square root of the eigenvalue of the covariance matrix.
• B. The correlation between predicted and observed values.
• C. The proportion of the variance in the dependent variable explained by the model.
• D. The total sum of squares divided by degrees of freedom.

Answer: (C)

R-squared measures how much of the variation in the dependent variable your model explains. It’s computed as 1 minus the ratio of the residual sum of squares (unexplained error) to the total sum of squares (overall variability in the data): R^2 = 1 - SSE/SST. So, if R^2 is high, the model captures most of the variance in y; if it’s low, a lot of variability remains unexplained by the predictors. In simple regression, R-squared is also the squared correlation between observed and predicted values, which can help intuition, but the precise interpretation is the proportion of explained variance. The other statements mix different concepts (like eigenvalues or just plain correlation) and don’t describe what R-squared represents.

R-squared measures how much of the variation in the dependent variable your model explains. It’s computed as 1 minus the ratio of the residual sum of squares (unexplained error) to the total sum of squares (overall variability in the data): R^2 = 1 - SSE/SST. So, if R^2 is high, the model captures most of the variance in y; if it’s low, a lot of variability remains unexplained by the predictors. In simple regression, R-squared is also the squared correlation between observed and predicted values, which can help intuition, but the precise interpretation is the proportion of explained variance. The other statements mix different concepts (like eigenvalues or just plain correlation) and don’t describe what R-squared represents.