What is the consequence of including too many predictors in a multiple linear regression model?

Including too many predictors in a multiple linear regression model can lead to several consequences that can significantly impact the model's performance and usefulness.

When discussing increased variance and potential overfitting, it's important to understand that as more predictors are added to the model, the model becomes more complex. This complexity can allow the model to fit the training data very well, capturing not just the underlying patterns but also the noise present in the data. Overfitting occurs when the model is overly tailored to the specific dataset used for training and fails to generalize well to new, unseen data. This results in high variance, where small changes in the input data can lead to large changes in the predicted outputs.

Additionally, the interpretability of the model is affected as more predictors are included. A model with many predictors can become cumbersome and difficult to understand or explain. It may obscure the relationship between the predictors and the target variable, making it challenging for stakeholders to gain insights or make informed decisions based on the model's results.

Lastly, while adding predictors can sometimes lead to improved accuracy on the training set, the increased complexity usually does not result in better performance on validation or test sets due to overfitting. Therefore, while it may seem intuitive that more predictors could improve the