Why do some regressions models give you r and some give you r squared?
What does r squared tell you?
If you take the square root of r squared for a model and get a number close to one does that mean that the closer the square root of r squared to one, it is the better model?
When it comes to regression models, there are different metrics used to evaluate their performance and understand how well they fit the data. The metrics commonly used for this purpose are the coefficient of correlation (r) and the coefficient of determination (r squared).
1. r (also known as the correlation coefficient) indicates the strength and direction of the linear relationship between the independent and dependent variables in a regression model. The value of r ranges from -1 to 1, where 1 indicates a strong positive linear relationship, -1 indicates a strong negative linear relationship, and 0 indicates no linear relationship.
2. r squared (also known as the coefficient of determination) is another important metric that is derived from r. It represents the proportion of variance in the dependent variable that can be explained by the independent variables in the regression model. The value of r squared ranges from 0 to 1. A higher r squared value indicates that a larger proportion of the variance is accounted for by the regression model.
To address your third question, taking the square root of r squared does not provide much useful information. The reason is that r squared is already a standardized metric and is directly interpretable. However, a high value of r squared (close to 1) indicates that the regression model explains a significant portion of the total variation in the dependent variable, suggesting a better fit of the model. Therefore, a larger r squared value indeed suggests a better model fit.
It's important to note that evaluating a regression model's performance is not solely based on r or r squared, as there are other aspects to consider such as significance of coefficients, residual analysis, and understanding the context of the data.