What does R-squared measure in a regression model?

What does R-squared measure in a regression model?

• A. The proportion of variance in the response explained by the model.
• B. The slope of the regression line.
• C. The probability that the null model is true.
• D. The correlation between predictor and outcome.

Answer: (A)

R-squared tells you how much of the variability in the response variable the model explains. It’s the proportion of total variation in the observed outcomes that the regression line (the model) accounts for. Formally, it’s 1 minus the sum of squared residuals (the unexplained variation) divided by the total sum of squares (the total variation in the data). So if the model fits the data well and the residuals are small, R-squared is close to 1; if the model doesn’t capture much of the variation, it’s closer to 0. In simple linear regression with an intercept, R-squared equals the square of the correlation between the predictor and the response, which ties the strength of the linear association to the amount of variance explained. But R-squared is not the slope of the regression line, nor a probability about the null model, and it’s not simply the plain correlation between predictor and outcome. It specifically quantifies explanatory power in terms of variance explained, with higher values indicating more of the response’s variability is captured by the model.

R-squared tells you how much of the variability in the response variable the model explains. It’s the proportion of total variation in the observed outcomes that the regression line (the model) accounts for. Formally, it’s 1 minus the sum of squared residuals (the unexplained variation) divided by the total sum of squares (the total variation in the data). So if the model fits the data well and the residuals are small, R-squared is close to 1; if the model doesn’t capture much of the variation, it’s closer to 0.

In simple linear regression with an intercept, R-squared equals the square of the correlation between the predictor and the response, which ties the strength of the linear association to the amount of variance explained. But R-squared is not the slope of the regression line, nor a probability about the null model, and it’s not simply the plain correlation between predictor and outcome. It specifically quantifies explanatory power in terms of variance explained, with higher values indicating more of the response’s variability is captured by the model.