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I'm performing linear regression to predict house prices. My dataset has close to 2,000 observations. My model has over 50 variables. I'd like to know how I can tune hyperparameters like, L2 regularization, and degree of polynomial used in the objective function. I'm aware only of k-fold cross validation to perform this task. Is it common to use cross-validation for this, or are there better or more common techniques?

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If you have enough, plenty of data, it is common to divide the dataset into 2, training set and validation set. You fit the model with the training sets and perform the tuning with the validation sets. It will be faster because you don't need to perform the validation k number of times. For smaller number of dataset, using cross validation will generalize better.

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