# Model performance metrics

In regression model, the most commonly known evaluation metrics.

## 1. Root Mean Squared Error(RMSE)

(RMSE), which measures the average error performed by the model in predicting the outcome for an observation. Mathematically, the RMSE is the square root of the mean squared error (MSE), which is the average squared difference between the observed actual outome values and the values predicted by the model.

## 2. Residual Standard Error (RSE)

RSE is known as sigma, is a variant of the RMSE adjusted for the number of predictors in the model. The lower the RSE, the better the model. In practice, the difference between RMSE and RSE is very small, particularly for large multivariate data.

## 3. R-squared (R2)

R Squared is also known as coefficient of determination, that is represented by R2 or r2 and call it as R Squared- is the number indicating the variance in the dependent variable that is to be predicted from the independent variable. It is a statistic model used for future prediction and outcomes, also regarded as testing of hypothesis.

The proportion of variation in the outcome that is explained by the predictor variables. In multiple regression models, R2 corresponds to the squared correlation between the observed outcome values and the predicted values by the model. The Higher the R-squared, the better the model.

### R-Square conditions

• The R-square is the square of the correlation(r), thus it ranges from 0 to 1.
• With linear regression, the correlation of determination is equal to the square of the correlation between the x and y variables.
• If R2 is equal to 0, then the dependent variable should not be predicted from the independent variable.
• If R2 is equal to 1, then the dependent variable should be predicted from the independent variable without any error.
• If R2 is between 0 and 1, then it indicates the extent that the dependent variable can be predictable. If R2 of 0.10 means, it is 10 per cent of the variance in y variable is predicted from the x variable. If 0.20 means, it is 20 per cent of the variance is y variable is predicted from the x variable, and so on.

something in the range 0.7-0.8, is a good model.. If R-squared = 1, means the model fits the data perfectly.

## 4. Mean Absolute Error (MAE)

MAE measures the average magnitude of the errors in a set of predictions, without considering their direction. Itâ€™s the average over the test sample of the absolute differences between prediction and actual observation where all individual differences have equal weight.