What is R² in Machine Learning and its 9 Key limitations!

In machine learning, R-squared (R²) is often used as a measure of the model’s goodness of fit, but it has limitations. It does not provide information about whether the model’s assumptions are met or whether it is the best model for the data.

R-squared (R²) is basically a statistical metric used to evaluate the goodness of fit of a regression model in machine learning and statistics.

It is also known as the coefficient of determination and is a commonly used measure to assess how well a regression model explains the variance in the dependent variable.

R-squared values typically range between 0 and 1, where:

• R² = 1: This indicates that the regression model perfectly fits the data, meaning it explains all of the variance in the dependent variable, and there is no error in the predictions.

• R² = 0: This means that the regression model does not explain any of the variance in the dependent variable, and its predictions are no better than simply using the mean of the dependent variable for all predictions.

• 0 < R² < 1: This indicates the proportion of the variance in the dependent variable that is explained by the independent variables included in the model. For example, an R² of 0.75 means that 75% of the variance in the dependent variable is explained by the model, while the remaining 25% is unexplained and is attributed to random error or other factors not considered in the model.

The formula for calculating R-squared is as follows:

R² =1− (SSR/SST)

Where:

SSR (Sum of Squared Residuals) is the sum of the squared differences between the actual values of the dependent variable and the predicted values by the model.

SST (Total Sum of Squares) is the sum of the squared differences between the actual values of the dependent variable and the mean of the dependent variable.

Additionally, R-squared can be misleading when applied to complex models with many predictors, as it may increase even when adding irrelevant predictors. Therefore, it should be used in conjunction with other evaluation metrics and domain knowledge to assess model performance comprehensively.

Lets understand more on Limitation of R-squared (R²) method:

While R-squared (R²) is a useful metric for evaluating the goodness of fit of a regression model, it has some limitations and drawbacks that you should be aware of:

1. Doesn’t Indicate Model Accuracy:

R-squared measures how well the model explains the variance in the dependent variable, but it doesn’t tell you whether the model’s predictions are accurate in an absolute sense. A high R-squared value doesn’t necessarily mean that the model’s predictions are always close to the actual values.

2. Sensitive to Outliers:

R-squared is sensitive to outliers in the data. A single outlier can significantly affect the R-squared value, potentially leading to an overestimation or underestimation of the model’s performance.

3. Doesn’t Detect Nonlinearity:

R-squared assumes a linear relationship between the independent and dependent variables. If the true relationship is nonlinear, a high R-squared value may still indicate a poor model fit.

4. No Information about Significance:

R-squared does not provide information about the statistical significance of the coefficients of the independent variables. It doesn’t tell you whether the relationships between predictors and the target variable are meaningful or just due to chance.

5. Inappropriate for Comparing Models:

R-squared should not be used as the sole metric for comparing different models. A model with a higher R-squared value might not necessarily be a better model for prediction or inference. Other metrics like Mean Squared Error (MSE), Root Mean Squared Error (RMSE), or cross-validation are more appropriate for model comparison.

6. Data Scaling Effects:

R-squared is sensitive to the scale of the data. Rescaling the dependent variable or independent variables can change the R-squared value without changing the underlying relationships in the data.

7. Overfitting:

High R-squared values can sometimes be a sign of overfitting, especially when you have a large number of predictors. Overfit models may perform well on the training data but generalize poorly to new, unseen data.

8. Multicollinearity:

R-squared doesn’t handle multicollinearity well. When independent variables are highly correlated with each other, R-squared can give a misleading impression of how well each variable contributes to explaining the variance in the dependent variable.

9. Assumes No Autocorrelation:

R-squared assumes that observations are independent. In time series data or spatial data, where observations may be correlated, R-squared may not be an appropriate measure.

To sum up, while R-squared is a valuable metric for assessing the goodness of fit of a regression model, it should be used alongside other evaluation metrics and a thorough understanding of the data and the problem domain. It is important to be aware of its limitations and to consider them when interpreting the results of your regression analysis.