In a regression output, what does a high R-squared value represent?

In a regression output, what does a high R-squared value represent?

• A. It indicates the strength of the linear relationship between predictors
• B. It is the probability that the model is correct
• C. It indicates the proportion of variance in the dependent variable explained by the model
• D. It is the correlation between predicted and actual values

Answer: (C)

The main concept being tested is what R-squared tells us about a regression model. A high R-squared means the model explains a large portion of the variability in the dependent variable. Put simply, it shows how much of the outcome’s differences across observations are accounted for by the predictors. For example, an R-squared of 0.8 implies that 80% of the variation in the dependent variable is explained by the model, while the remaining 20% is due to factors not captured by the model or random variation. This is the best answer because it directly describes the proportion of variance explained by the model, which is exactly what R-squared measures. The idea that R-squared represents the strength of the linear relationship between predictors belongs to a different concept (the relationship among predictors is not the same as how much of the outcome’s variability the model explains). The notion that it is a probability the model is correct is a common misinterpretation; R-squared is not a probability. The notion that it is the correlation between predicted and actual values is related in simple cases but not the formal definition; R-squared specifically reflects explained variance, not just correlation.

The main concept being tested is what R-squared tells us about a regression model. A high R-squared means the model explains a large portion of the variability in the dependent variable. Put simply, it shows how much of the outcome’s differences across observations are accounted for by the predictors. For example, an R-squared of 0.8 implies that 80% of the variation in the dependent variable is explained by the model, while the remaining 20% is due to factors not captured by the model or random variation.

This is the best answer because it directly describes the proportion of variance explained by the model, which is exactly what R-squared measures. The idea that R-squared represents the strength of the linear relationship between predictors belongs to a different concept (the relationship among predictors is not the same as how much of the outcome’s variability the model explains). The notion that it is a probability the model is correct is a common misinterpretation; R-squared is not a probability. The notion that it is the correlation between predicted and actual values is related in simple cases but not the formal definition; R-squared specifically reflects explained variance, not just correlation.