Linear Regression with Two Predictor Variables:
In this type of regression, we use two predictor variables, X1 and X2, to predict an outcome variable, Y. We’re not only interested in their individual effects but also in how they interact (X1*X2) and if there are any quadratic effects. This allows us to create a more complex model that considers how these variables work together to give desired outcome as Y.
Y = β0 + β1*X1 + β2*X2 + β3*X1*X2 + ε
Where Y is the value that we are going to predict.
X1 and X2 are two predictor variables. β0 is the intercept term. β1 and β2 are the coefficients for the linear effects of X1 and X2. β3 represents the coefficient for the interaction term (X1*X2). ε is the error term.
Overfitting: Overfitting happens when our model works really well on the data it was trained on (the data it knows) but doesn’t perform well on new, unseen data. This defines Overfitting of a model.
Cross-Validation:
Cross-validation is an excellent way to deal with overfitting. Imagine that we have a big dataset, and we divided it into smaller chunks. Then train and test the model multiple times, using different chunks for testing each time. This helps us to see how well our designed model performs on different parts of the data. This is how the cross validation has been done completely.