When there are two or more independent variables, it is called multiple regression.

Multiple linear regression is used to evaluate the influence of one independent variable on another. A researcher may claim a causal relationship between variables if one variable influences another. The average value of a given set of data is the mode.

Linear regression can only be used when one has two continuous variables—an independent variable and a dependent variable. The independent variable is the parameter that is used to calculate the dependent variable or outcome. A multiple regression model extends to several explanatory variables.

Simulation studies show that a good rule of thumb is to have 10-15 observations per term in multiple linear regression. For example, if your model contains two predictors and the interaction term, you’ll need 30-45 observations.

To avoid overfitting a regression model, you should draw a random sample that is large enough to handle all of the terms that you expect to include in your model. This process requires that you investigate similar studies before you collect data.

One way of looking at this is the classic view in machine learning theory that the more parameters your model has, the more data you need to fit those properly. This is a good and useful view. Using linear regression allows us to sacrifice flexibility to get a better fit from less data. Consider again the same line.

Overfitting occurs when too many variables are included in the model and the model appears to fit well to the current data. Because some of variables retained in the model are actually noise variables, the model cannot be validated in future dataset.

In regression analysis, overfitting occurs frequently. As an extreme example, if there are p variables in a linear regression with p data points, the fitted line can go exactly through every point.

The problem of overfitting is possible in linear regression if we add too many features compare to the number of training set. Which may force our model to fit to the training set rather than the actual domain.

In addition, the following ways can also be used to tackle underfitting.

1. Increase the size or number of parameters in the ML model.
2. Increase the complexity or type of the model.
3. Increasing the training time until cost function in ML is minimised.

The best solution to an overfitting problem is avoidance. Identify the important variables and think about the model that you are likely to specify, then plan ahead to collect a sample large enough handle all predictors, interactions, and polynomial terms your response variable might require.

How to Prevent Overfitting

1. Cross-validation. Cross-validation is a powerful preventative measure against overfitting.
2. Train with more data. It won’t work every time, but training with more data can help algorithms detect the signal better.
3. Remove features.
4. Early stopping.
5. Regularization.
6. Ensembling.

Overfitting is a modeling error in statistics that occurs when a function is too closely aligned to a limited set of data points. Thus, attempting to make the model conform too closely to slightly inaccurate data can infect the model with substantial errors and reduce its predictive power.

Handling overfitting

1. Reduce the network’s capacity by removing layers or reducing the number of elements in the hidden layers.
2. Apply regularization , which comes down to adding a cost to the loss function for large weights.
3. Use Dropout layers, which will randomly remove certain features by setting them to zero.

In linear regression overfitting occurs when the model is “too complex”. This usually happens when there are a large number of parameters compared to the number of observations. Such a model will not generalise well to new data. That is, it will perform well on training data, but poorly on test data.

The common pattern for overfitting can be seen on learning curve plots, where model performance on the training dataset continues to improve (e.g. loss or error continues to fall or accuracy continues to rise) and performance on the test or validation set improves to a point and then begins to get worse.

Overfitting is easy to diagnose with the accuracy visualizations you have available. If “Accuracy” (measured against the training set) is very good and “Validation Accuracy” (measured against a validation set) is not as good, then your model is overfitting.

Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data. This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model.

With these techniques, you should be able to improve your models and correct any overfitting or underfitting issues….Handling Underfitting:

1. Get more training data.
2. Increase the size or number of parameters in the model.
3. Increase the complexity of the model.
4. Increasing the training time, until cost function is minimised.

How to Prevent Overfitting or Underfitting

1. Cross-validation:
2. Train with more data.
3. Data augmentation.
4. Reduce Complexity or Data Simplification.
5. Ensembling.
6. Early Stopping.
7. You need to add regularization in case of Linear and SVM models.
8. In decision tree models you can reduce the maximum depth.

Using a more complex model, for instance by switching from a linear to a non-linear model or by adding hidden layers to your neural network, will very often help solve underfitting. The algorithms you use include by default regularization parameters meant to prevent overfitting.

All machine learning algorithms, boosting included, can overfit. Of course, standard multivariate linear regression is guaranteed to overfit due to Stein’s phenomena. For boosting specifically: to combat overfitting is usually as simple as using cross validation to determine how many boosting steps to take.

5 Techniques to Prevent Overfitting in Neural Networks

1. Simplifying The Model. The first step when dealing with overfitting is to decrease the complexity of the model.
2. Early Stopping. Early stopping is a form of regularization while training a model with an iterative method, such as gradient descent.
3. Use Data Augmentation.
4. Use Regularization.
5. Use Dropouts.

Random Forests do not overfit. The testing performance of Random Forests does not decrease (due to overfitting) as the number of trees increases. Hence after certain number of trees the performance tend to stay in a certain value.

2 Answers

1. The “strength” of the “weak” learners: If you use very simple weak learners, such as decision stumps (1-level decision trees), then the algorithms are much less prone to overfitting.
2. The noise level in the data: AdaBoost is particularly prone to overfitting on noisy datasets.

Bagging and Boosting decrease the variance of your single estimate as they combine several estimates from different models. So the result may be a model with higher stability. However, Boosting could generate a combined model with lower errors as it optimises the advantages and reduces pitfalls of the single model.