Mengestimasi Kemiringan & Intersep Secara Visual

Membangun model linear adalah cara otomatis untuk melakukan sesuatu yang sebenarnya dapat kita lakukan secara "manual" dengan visualisasi data dan banyak coba-coba. Metode visual bukan yang paling efisien atau presisi, tetapi memang sangat membantu mengilustrasikan konsep, jadi mari kita mencobanya!

Diberikan beberapa data hasil pengukuran, tujuan Anda adalah menebak nilai kemiringan (slope) dan intersep, memasukkannya ke dalam model, lalu menyesuaikan tebakan sampai model yang dihasilkan sesuai dengan data. Gunakan data yang disediakan xd, yd, serta fungsi model() yang disediakan untuk membuat prediksi model. Bandingkan prediksi dengan data menggunakan plot_data_and_model() yang telah disediakan.

Latihan ini adalah bagian dari kursus

Pengantar Pemodelan Linear di Python

Petunjuk latihan

Amati grafik di atas, lalu berikan perkiraan awal untuk trial_slope dan trial_intercept. Ini dapat Anda sesuaikan nanti dalam latihan.
Gunakan fungsi yang sudah didefinisikan xm, ym = model(intercept, slope) untuk menghasilkan prediksi model.
Gunakan fungsi fig = plot_data_and_model(xd, yd, xm, ym) yang disediakan untuk memplot data terukur (xd, yd) dan prediksi hasil pemodelan (xm, ym) secara bersamaan.
Jika model belum sesuai dengan data, coba nilai lain untuk trial_slope dan trial_intercept lalu jalankan ulang kode Anda.
Ulangi hingga Anda yakin telah mendapatkan nilai terbaik, lalu tetapkan ke final_slope dan final_intercept dan Kirim Jawaban Anda.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Look at the plot data and guess initial trial values
trial_slope = ____
trial_intercept = ____

# input thoses guesses into the model function to compute the model values.
xm, ym = ____(trial_intercept, trial_slope)

# Compare your your model to the data with the plot function
fig = ____(xd, yd, xm, ym)
plt.show()

# Repeat the steps above until your slope and intercept guess makes the model line up with the data.
final_slope = ____
final_intercept = ____

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Pengantar Pemodelan Linear di Python

SkillTag.level.intermediateSkillTag.label

4.7+

Mulai Kursus Gratis

We start the course with an initial exploration of linear relationships, including some motivating examples of how linear models are used, and demonstrations of data visualization methods from matplotlib. We then use descriptive statistics to quantify the shape of our data and use correlation to quantify the strength of linear relationships between two variables.

Exercise 1: Pengantar Pemodelan Data Exercise 2: Alasan Melakukan Pemodelan: Interpolasi Exercise 3: Alasan Melakukan Pemodelan: Ekstrapolasi Exercise 4: Alasan Melakukan Pemodelan: Mengestimasi Hubungan Exercise 5: Memvisualisasikan Hubungan Linear Exercise 6: Memplot Data Exercise 7: Memplot Model pada Data Exercise 8: Mengestimasi Kemiringan & Intersep Secara Visual

Latihan Saat Ini

Exercise 9: Mengkuantifikasi Hubungan Linear Exercise 10: Mean, Deviasi, & Standar Deviasi Exercise 11: Kovarians vs Korelasi Exercise 12: Kekuatan Korelasi

Here we look at the parts that go into building a linear model. Using the concept of a Taylor Series, we focus on the parameters slope and intercept, how they define the model, and how to interpret the them in several applied contexts. We apply a variety of python modules to find the model that best fits the data, by computing the optimal values of slope and intercept, using least-squares, numpy, statsmodels, and scikit-learn.

Exercise 1: What makes a model linear Exercise 2: Terms in a Model Exercise 3: Model Components Exercise 4: Model Parameters Exercise 5: Interpreting Slope and Intercept Exercise 6: Linear Proportionality Exercise 7: Slope and Rates-of-Change Exercise 8: Intercept and Starting Points Exercise 9: Model Optimization Exercise 10: Residual Sum of the Squares Exercise 11: Minimizing the Residuals Exercise 12: Visualizing the RSS Minima Exercise 13: Least-Squares Optimization Exercise 14: Least-Squares with `numpy`Exercise 15: Optimization with Scipy Exercise 16: Least-Squares with `statsmodels`

Next we will apply models to real data and make predictions. We will explore some of the most common pit-falls and limitations of predictions, and we evaluate and compare models by quantifying and contrasting several measures of goodness-of-fit, including RMSE and R-squared.

Exercise 1: Modeling Real Data Exercise 2: Linear Model in Anthropology Exercise 3: Linear Model in Oceanography Exercise 4: Linear Model in Cosmology Exercise 5: The Limits of Prediction Exercise 6: Interpolation: Inbetween Times Exercise 7: Extrapolation: Going Over the Edge Exercise 8: Goodness-of-Fit Exercise 9: RMSE Step-by-step Exercise 10: R-Squared Exercise 11: Standard Error Exercise 12: Variation Around the Trend Exercise 13: Variation in Two Parts

In our final chapter, we introduce concepts from inferential statistics, and use them to explore how maximum likelihood estimation and bootstrap resampling can be used to estimate linear model parameters. We then apply these methods to make probabilistic statements about our confidence in the model parameters.

Exercise 1: Inferential Statistics Concepts Exercise 2: Sample Statistics versus Population Exercise 3: Variation in Sample Statistics Exercise 4: Visualizing Variation of a Statistic Exercise 5: Model Estimation and Likelihood Exercise 6: Estimation of Population Parameters Exercise 7: Maximizing Likelihood, Part 1 Exercise 8: Maximizing Likelihood, Part 2 Exercise 9: Model Uncertainty and Sample Distributions Exercise 10: Bootstrap and Standard Error Exercise 11: Estimating Speed and Confidence Exercise 12: Visualize the Bootstrap Exercise 13: Model Errors and Randomness Exercise 14: Test Statistics and Effect Size Exercise 15: Null Hypothesis Exercise 16: Visualizing Test Statistics Exercise 17: Visualizing the P-Value Exercise 18: Course Conclusion