Correlatie en R-kwadraat

De lineaire correlatie van twee variabelen, \(x\) en \(y\), meet de sterkte van de lineaire relatie tussen die twee. Wanneer \(x\) en \(y\) respectievelijk:

de uitkomsten zijn van een regressiemodel dat de kwadratische fout minimaliseert (zoals lineaire regressie) en
de echte uitkomsten van de trainingsdata,

dan is het kwadraat van de correlatie gelijk aan \(R^2\). Dat ga je in deze oefening controleren.

unemployment en unemployment_model zijn voor je beschikbaar.

Deze oefening maakt deel uit van de cursus

Supervised Learning in R: Regressie

Cursus bekijken

Oefeninstructies

Gebruik cor() (docs) om de correlatie tussen de voorspellingen en vrouwelijke werkloosheid te krijgen. Sla deze op in de variabele rho en print hem. Zorg dat je de Pearson-correlatie gebruikt (de standaard).
Kwadreer rho en sla dit op in rho2. Print het.
Vergelijk rho2 met \(R^2\) uit het model (met glance()). Is het hetzelfde?

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# unemployment is available
summary(unemployment)

# unemployment_model is available
summary(unemployment_model)

# Get the correlation between the prediction and true outcome: rho and print it
(rho <- ___)

# Square rho: rho2 and print it
(rho2 <- ___)

# Get R-squared from glance and print it
(rsq_glance <- ___(___)$___)

Code bewerken en uitvoeren

Deze oefening maakt deel uit van de cursus

Supervised Learning in R: Regressie

SkillTag.level.intermediateSkillTag.label

4.6+

Begin de cursus gratis

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: Een model grafisch evalueren Exercise 2: Beoordeel het werkloosheidsmodel grafisch Exercise 3: De gain-curve om het werkloosheidsmodel te evalueren Exercise 4: Root Mean Squared Error (RMSE)Exercise 5: RMSE berekenen Exercise 6: R-kwadraat Exercise 7: R-squared berekenen Exercise 8: Correlatie en R-kwadraat

Huidige oefening

Exercise 9: Een model goed trainen Exercise 10: Een willekeurige test/train-split maken Exercise 11: Train een model met een test/train-split Exercise 12: Evalueer een model met een train/test-split Exercise 13: Maak een cross-validatieplan Exercise 14: Evalueer een modelleringsprocedure met n-voudige crossvalidatie

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 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