Below mentioned the measure of performance of a linear regression model. But the utilities are different.

Implementation in Python (sklearn - https://scikit-learn.org/stable/modules/model_evaluation.html):

Hope it help.

As Anant Prakash Awasthi suggests there are many and there purposes are usually different. I like the validation section of this book: Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating | Ewout W. Steyerberg | download (b-ok.cc) Good luck, David Booth

Rather than trying to getting some number of statistics, why don't you say what characteristics that you are trying to maximize/minimize? It seems very silly just trying to get some number of statistics rather than being guiding by what you want.

The choice of the error metric you use to evaluate predictions depends on the loss function you used to find predictions (see page 3 of Davydenko and Fildes, 2016):

Chapter Forecast Error Measures: Critical Review and Practical Recommendations

If you want to go deep into error metrics and loss functions, please let me recommend my PhD thesis (Davydenko, 2012):

Thesis Integration of judgmental and statistical approaches for dem...

In section 3.2.4. "Finding Optimal Point Forecasts and Estimating Systematic Errors" you'll find discussion of how to find optimal forecasts depending on the loss function. Basically, it has been well-known since Zellner (1971): if you want optimal estimates in terms of MAE, you need the median of forecast density, if you want optimal estimates in terms of MSE, you need the mean.

In (Davydenko and Fildes, 2016) you'll find an overview of alternative error estimators (including the RMSE and MAPE). However, as we show, MAPE is not advisable as it may give misleading results.

Usually, the best choice is the out-of-sample MAE. Reasons: simple to interpret and corresponds to the loss function used to optimize forecasts even after back-transformations (see Davydenko and Fildes, 2016, p.3).

To average MAEs we recommend the AvgRelMAE, see the relevant section in (Davydenko and Fildes, 2016).

Generally, the use of a range of alternative metrics is not a good approach: you need the metric that reflects the loss function you used to optimize predictions.

For a framework to evaluate predictions I recommend this work:

Conference Paper Data Formats and Visual Tools for Forecast Evaluation in Cyb...