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  3. Supervised Learning in R: Regression
  • 1

    What is Regression?

    Free

    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.

  • 2

    Training and Evaluating Regression Models

    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.

  • 3

    Issues to Consider

    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.

  • 4

    Dealing with Non-Linear Responses

    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.

  • 5

    Tree-Based Methods

    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.

Initializing

Exercise

Input transforms: the "hockey stick"

In this exercise, we will build a model to predict price from a measure of the house's size (surface area). The houseprice dataset, loaded for you, has the columns:

  • price: house price in units of $1000
  • size: surface area

A scatterplot of the data shows that the data is quite non-linear: a sort of "hockey-stick" where price is fairly flat for smaller houses, but rises steeply as the house gets larger. Quadratics and tritics are often good functional forms to express hockey-stick like relationships. Note that there may not be a "physical" reason that price is related to the square of the size; a quadratic is simply a closed form approximation of the observed relationship.

scatterplot

You will fit a model to predict price as a function of the squared size, and look at its fit on the training data.

Because ^ is also a symbol to express interactions, use the function I() (docs) to treat the expression x^2 “as is”: that is, as the square of x rather than the interaction of x with itself.

exampleFormula = y ~ I(x^2)

Instructions

100 XP
  • Write a formula, fmla_sqr, to express price as a function of squared size. Print it.
  • Fit a model model_sqr to the data using fmla_sqr
  • For comparison, fit a linear model model_lin to the data using the formula price ~ size.
  • Fill in the blanks to
    • make predictions from the training data from the two models
    • pivot the predictions into a single column pred using pivot_longer().
    • graphically compare the predictions of the two models to the data. Which fits better?