When comparing two simple linear regression models, which model is preferred if one has an R-squared of 0.58, and the other has 0.89?

When comparing two simple linear regression models, which model is preferred if one has an R-squared of 0.58, and the other has 0.89?

• A. Model 1 with R-squared of 0.58
• B. Model 2 with R-squared of 0.89
• C. Both models are equivalent
• D. None of the models can be evaluated

Answer: (B)

The preference for Model 2 with an R-squared of 0.89 over Model 1 with an R-squared of 0.58 is based on the interpretation of the R-squared statistic in linear regression. R-squared measures the proportion of variance in the dependent variable that can be explained by the independent variable(s) in the model. A higher R-squared value indicates that a greater amount of variance is accounted for by the model, suggesting it fits the data better. In this case, Model 2 explains 89% of the variance in the dependent variable, while Model 1 explains only 58%. This significant difference means that Model 2 is likely more predictive and provides a better fit to the data, making it the preferred choice when evaluating these two models. It’s important to note that while R-squared is a useful metric for model evaluation, it is not the sole criterion for determining the best model. Factors such as the significance of predictors, potential overfitting, and the context of the analysis should also be considered. However, based on the R-squared values alone, Model 2 is clearly superior in terms of explained variance.

The preference for Model 2 with an R-squared of 0.89 over Model 1 with an R-squared of 0.58 is based on the interpretation of the R-squared statistic in linear regression. R-squared measures the proportion of variance in the dependent variable that can be explained by the independent variable(s) in the model. A higher R-squared value indicates that a greater amount of variance is accounted for by the model, suggesting it fits the data better.

In this case, Model 2 explains 89% of the variance in the dependent variable, while Model 1 explains only 58%. This significant difference means that Model 2 is likely more predictive and provides a better fit to the data, making it the preferred choice when evaluating these two models.

It’s important to note that while R-squared is a useful metric for model evaluation, it is not the sole criterion for determining the best model. Factors such as the significance of predictors, potential overfitting, and the context of the analysis should also be considered. However, based on the R-squared values alone, Model 2 is clearly superior in terms of explained variance.