Modeling an interaction

In this exercise, you will use interactions to model the effect of gender and gastric activity on alcohol metabolism.

The alcohol data frame has been pre-loaded, and has the columns:

Metabol: the alcohol metabolism rate
Gastric: the rate of gastric alcohol dehydrogenase activity
Sex: the sex of the drinker (Male or Female)

In the video, we fit three models to the alcohol data:

one with only additive (main effect) terms : Metabol ~ Gastric + Sex
two models, each with interactions between gastric activity and sex

You saw that one of the models with interaction terms had a better R-squared than the additive model, suggesting that using interaction terms gives a better fit. In this exercise, you will compare the R-squared of one of the interaction models to the main-effects-only model.

Recall that the operator : designates the interaction between two variables. The operator * designates the interaction between the two variables, plus the main effects.

x*y = x + y + x:y

This exercise is part of the course

Supervised Learning in R: Regression

Exercise instructions

Write a formula that expresses Metabol as a function of Gastric and Sex with no interactions.
- Assign the formula to the variable fmla_add and print it.
Write a formula that expresses Metabol as a function of the interaction between Gastric and Sex.
- Add Gastric as a main effect, but not Sex.
- Assign the formula to the variable fmla_interaction and print it.
Fit a linear model with only main effects: model_add to the data.
Fit a linear model with the interaction: model_interaction to the data.
Call summary() on both models. Which has a better R-squared?

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# alcohol is available
summary(alcohol)

# Create the formula with main effects only
(fmla_add <- ___ )

# Create the formula with interactions
(fmla_interaction <- ___ )

# Fit the main effects only model
model_add <- ___

# Fit the interaction model
model_interaction <- ___

# Call summary on both models and compare
___
___

Edit and Run Code

This exercise is part of the course

Supervised Learning in R: Regression

IntermediateSkill Level

4.8+

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In this chapter we introduce the concept of regression from a machine learning point of view. We will present the fundamental regression method: linear regression. We will show how to fit a linear regression model and to make predictions from the model.

Exercise 1: Welcome and Introduction Exercise 2: Identify the regression tasks Exercise 3: Linear regression - the fundamental method Exercise 4: Code a simple one-variable regression Exercise 5: Examining a model Exercise 6: Predicting once you fit a model Exercise 7: Predicting from the unemployment model Exercise 8: Multivariate linear regression (Part 1)Exercise 9: Multivariate linear regression (Part 2)Exercise 10: Wrapping up linear regression

Now that we have learned how to fit basic linear regression models, we will learn how to evaluate how well our models perform. We will review evaluating a model graphically, and look at two basic metrics for regression models. We will also learn how to train a model that will perform well in the wild, not just on training data. Although we will demonstrate these techniques using linear regression, all these concepts apply to models fit with any regression algorithm.

Exercise 1: Evaluating a model graphically Exercise 2: Graphically evaluate the unemployment model Exercise 3: The gain curve to evaluate the unemployment model Exercise 4: Root Mean Squared Error (RMSE)Exercise 5: Calculate RMSE Exercise 6: R-squared Exercise 7: Calculate R-squared Exercise 8: Correlation and R-squared Exercise 9: Properly Training a Model Exercise 10: Generating a random test/train split Exercise 11: Train a model using test/train split Exercise 12: Evaluate a model using test/train split Exercise 13: Create a cross validation plan Exercise 14: Evaluate a modeling procedure using n-fold cross-validation

Before moving on to more sophisticated regression techniques, we will look at some other modeling issues: modeling with categorical inputs, interactions between variables, and when you might consider transforming inputs and outputs before modeling. While more sophisticated regression techniques manage some of these issues automatically, it's important to be aware of them, in order to understand which methods best handle various issues -- and which issues you must still manage yourself.

Exercise 1: Categorical inputs Exercise 2: Examining the structure of categorical inputs Exercise 3: Modeling with categorical inputs Exercise 4: Interactions Exercise 5: Modeling an interaction

Current Exercise

Exercise 6: Modeling an interaction (2)Exercise 7: Transforming the response before modeling Exercise 8: Relative error Exercise 9: Modeling log-transformed monetary output Exercise 10: Comparing RMSE and root-mean-squared Relative Error Exercise 11: Transforming inputs before modeling Exercise 12: Input transforms: the "hockey stick"Exercise 13: Input transforms: the "hockey stick" (2)

Now that we have mastered linear models, we will begin to look at techniques for modeling situations that don't meet the assumptions of linearity. This includes predicting probabilities and frequencies (values bounded between 0 and 1); predicting counts (nonnegative integer values, and associated rates); and responses that have a non-linear but additive relationship to the inputs. These algorithms are variations on the standard linear model.

Exercise 1: Logistic regression to predict probabilities Exercise 2: Fit a model of sparrow survival probability Exercise 3: Predict sparrow survival Exercise 4: Poisson and quasipoisson regression to predict counts Exercise 5: Poisson or quasipoisson Exercise 6: Fit a model to predict bike rental counts Exercise 7: Predict bike rentals on new data Exercise 8: Visualize the bike rental predictions Exercise 9: GAM to learn non-linear transforms Exercise 10: Writing formulas for GAM models Exercise 11: Writing formulas for GAM models (2)Exercise 12: Model soybean growth with GAM Exercise 13: Predict with the soybean model on test data

In this chapter we will look at modeling algorithms that do not assume linearity or additivity, and that can learn limited types of interactions among input variables. These algorithms are *tree-based* methods that work by combining ensembles of *decision trees* that are learned from the training data.

Exercise 1: The intuition behind tree-based methods Exercise 2: Predicting with a decision tree Exercise 3: Random forests Exercise 4: Build a random forest model for bike rentals Exercise 5: Predict bike rentals with the random forest model Exercise 6: Visualize random forest bike model predictions Exercise 7: One-Hot-Encoding Categorical Variables Exercise 8: vtreat on a small example Exercise 9: Novel levels Exercise 10: vtreat the bike rental data Exercise 11: Gradient boosting machines Exercise 12: Find the right number of trees for a gradient boosting machine Exercise 13: Fit an xgboost bike rental model and predict Exercise 14: Evaluate the xgboost bike rental model Exercise 15: Visualize the xgboost bike rental model