How can you increase the variance explained in your statistical model?

To increase variance explained in a statistical model > Include relevant predictors to capture more variability. > Use advanced modeling techniques like ensemble methods or non-linear models. > Optimize model hyperparameters for better fit. > Address multicollinearity among predictors. > Collect more data to improve model precision. > Perform feature engineering to create informative variables. > By implementing these strategies, you can enhance the model's ability to explain variance in the data.

I agree with this, including additional relevant predictors can help explain the variance. Imagine you’re trying to predict a student’s final exam score. Initially you might only consider their performance in midterms. However by adding more variables such as hours spent studying, attendance in class, etc the model can better predict the final exam score as these factors can also influence exam performance. However you need to be cautious of overfitting.

Variance is calculated by finding the average of each data point's squared difference from the mean. We can increase variance by the following methods- 1.Increasing the Range of Data Points 2. Introducing Outliers 3. Increasing sample size

We can also increase the variance by modifying the distribution of the data points. For example, if our data follows a normal distribution, we can transform it to have a more skewed or leptokurtic distribution.Such distributions have a higher likelihood of extreme values, which can increase the variance.

Transforming existing variables or creating new ones through domain knowledge can uncover effects which were not previously modeled. For instance, for predicting house prices, you have data of house age and size. By creating an new feature such as age-size ratio (age of the house divided by its size), it can capture the effect of large sized older homes which are usually less desirable and attract comparatively lower prizes. The drawback to this approach is that it requires domain knowledge to come up with such features.

If we are working with a regression model, including interaction terms can increase the variance. Interaction terms capture the combined effect of two or more variables and can introduce additional variability into the model

The biggest dilemma, balancing under fitting and over fitting. Regularization, particularly Lasso is my go to approach as it is capable of shrinking features on its own. This can definitely help enhance the model’s performance but there isn’t one straight formula for this. I’ve found utilizing cross-validation with lasso be a good approach to find the optimal lambda value which minimizes overfitting while maintaining the model’s ability to generalize well to new data.

Regularization techniques are commonly used in machine learning to prevent overfitting and improve the generalization ability of models. 1. L1 Regularization (Lasso): L1 regularization adds a penalty term to the loss function that encourages the model to use fewer features by shrinking the less important feature coefficients to zero. 2. L2 Regularization (Ridge): L2 regularization adds a penalty term to the loss function that encourages the model to have smaller weights by shrinking the weight values.

Dropout: Dropout is a regularization technique commonly used in neural networks. It randomly sets a fraction of the input units to zero during training, which helps prevent the network from relying too heavily on any particular feature.

A model should be parisomnious, it means including several explanatory variables does not guarantee higher variance explained. There is should first be a economic theory that justifies the inclusion of an independent variable in model. The adjusted R square penalise the model for including variables which does not add much to the explanatory power of the model. Hence before choosing any independent variable first check for the theory and evidences of strong association with dependent variable.

Check your model for lack-of-fit. When pure error variance is near to the variance about the model, there is almost nothing more to be done. Steps 1, 2, 3, 4, and 6 are finished. Consider the potential value of data quality for any further improvement possibility. Model lack-of-fit can be checked approximately even when replicate points are not available for estimation of pure-error. The paper, Estimating pure-error from near replicates in design of experiments Publication: Journal of Quality Technology Date: January 2022 Issue: Volume 54 Issue 1 Pages: pp. 102-117 Author(s): King, Caleb, Bzik, Thomas, Parker, Peter describes how this can be done even outside of the design of experiments context.