# Linear Regression - Metrics to consider?

While evaluating the Linear regression model, which metric do we need to consider R square or Mean Squared Error (or which needs to be given more importance)?

Thank you.

• it completely depends on your choice.. but it's better to use mse or rmse or mae Apr 12, 2018 at 5:00

Aditya already mentioned rightly so in the comments RMSE, MSE or MAE is preferred while evaluating a linear regression model. So to answer your questions I will provide with the pros and cons of using RMSE and MAE and further more put forward some points to why R-squared is not preferred.

1. MAE vs. RMSE - Which metric is better ?

Ideally this depends on the loss function of your model, the most common one being L2 - euclidean distance (you can create your own loss function too). RMSE gives relatively higher weight to large errors. It does not necessarily increase with the variance of the errors but increases with the variance of the frequency distribution of error magnitudes. While, MAE is comparatively steady.

typically, it makes more sense to give a higher weight to points away from the mean in which RMSE would be preferred. In a scenario where being away from the mean by any magnitude would be penalized equally, MAE would be preferred.

RMSE can be troublesome when calculating on different sized test samples (As is the case when training a model). RMSE has a tendency to be increasingly larger than MAE as the test sample size increases ([RMSE] ≤ [MAE * sqrt(n)].

2. Is R-squared useless ? (Kinda harsh but sorry not sorry)

To keep it short and simple.

• R-squared does not measure goodness of fit.
• R-squared does not measure predictive error.
• R-squared does not allow you to compare models using transformed responses.
• R-squared does not measure how one variable explains another.
• Well written answer(+1) Apr 15, 2018 at 15:20
• Why do you say that $R^2$ is so useless when it is proportional to $MSE$? I am with you that it gives no additional information beyond $MSE$, and I even think that it can mislead people into thinking that $R^2=0.55$ is terrible since $55\%$ in school is an $\text{F}$ grade, but why do you say $R^2$ does not measure what $MSE$ does measure?
– Dave
Mar 3, 2021 at 17:55