Hitung R-squared

Sekarang setelah Anda menghitung RMSE dari prediksi model Anda, Anda akan menilai seberapa baik model menyesuaikan data: yaitu, seberapa besar ragam yang dijelaskan model. Anda dapat melakukannya menggunakan \(R^2\).

Misalkan \(y\) adalah nilai keluaran sebenarnya, \(p\) adalah prediksi dari model, dan \(res = y - p\) adalah residual dari prediksi.

Kemudian jumlah kuadrat total \(tss\) ("total variance") dari data adalah:

$$ tss = \sum{(y - \overline{y})^2} $$

di mana \(\overline{y}\) adalah nilai rata-rata dari \(y\).

Jumlah kuadrat galat residual model, \(rss\) adalah: $$ rss = \sum{res^2} $$

\(R^2\) (R-squared), yaitu "ragam yang dijelaskan" oleh model, adalah:

$$ 1 - \frac{rss}{tss} $$

Setelah Anda menghitung \(R^2\), Anda akan membandingkan hasil perhitungan Anda dengan \(R^2\) yang dilaporkan oleh glance() (docs). glance() mengembalikan data frame satu baris; untuk model regresi linear, salah satu kolom yang dikembalikan adalah \(R^2\) model pada data pelatihan.

Data frame unemployment telah dimuat untuk Anda, dan berisi kolom predictions dan residuals yang Anda hitung pada latihan sebelumnya. unemployment_model juga tersedia untuk Anda gunakan.

Latihan ini adalah bagian dari kursus

Supervised Learning di R: Regresi

Petunjuk latihan

Hitung rata-rata female_unemployment dan tetapkan ke variabel fe_mean.
Hitung jumlah kuadrat total dan tetapkan ke variabel tss.
Hitung jumlah kuadrat residual dan tetapkan ke variabel rss.
Hitung \(R^2\). Apakah modelnya sesuai dengan baik (\(R^2\) mendekati 1)?
Gunakan glance() untuk mendapatkan \(R^2\) dari model. Apakah sama dengan yang Anda hitung?

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# unemployment is available
summary(unemployment)

# unemployment_model is available
summary(unemployment_model)

# Calculate and print the mean female_unemployment: fe_mean
(fe_mean <- ___)

# Calculate and print the total sum of squares: tss
(tss <- ___((___ - ___)^2))

# Calculate and print residual sum of squares: rss
(rss <- ___)

# Calculate and print the R-squared: rsq
(rsq <- ___)

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

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Supervised Learning di R: Regresi

SkillTag.level.intermediateSkillTag.label

4.6+

Mulai Kursus 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: Mengevaluasi model secara grafis Exercise 2: Evaluasi model pengangguran secara grafis Exercise 3: Kurva gain untuk mengevaluasi model pengangguran Exercise 4: Root Mean Squared Error (RMSE)Exercise 5: Hitung RMSE Exercise 6: R-squared Exercise 7: Hitung R-squared

Latihan Saat Ini

Exercise 8: Korelasi dan R-squared Exercise 9: Melatih Model dengan Tepat Exercise 10: Membuat pembagian acak data train/test Exercise 11: Latih model menggunakan pemisahan test/train Exercise 12: Evaluasi model menggunakan pembagian train/test Exercise 13: Buat rencana cross validation Exercise 14: Evaluasi prosedur pemodelan menggunakan 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 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