Alasan Melakukan Pemodelan: Ekstrapolasi

Penggunaan pemodelan yang umum lainnya adalah ekstrapolasi untuk memperkirakan nilai data yang berada "di luar" atau "melewati" rentang (nilai min dan maks dari time) data terukur. Pada latihan ini, kita memiliki jarak yang diukur untuk waktu 0 hingga 5 jam, tetapi kita ingin memperkirakan seberapa jauh kita akan menempuh dalam 8 jam. Menggunakan himpunan data yang sama dari latihan sebelumnya, kami telah menyiapkan model linear distance = model(time). Gunakan model() tersebut untuk membuat prediksi tentang jarak yang ditempuh untuk waktu yang jauh lebih besar daripada waktu lain dalam pengukuran.

context figure

Latihan ini adalah bagian dari kursus

Pengantar Pemodelan Linear di Python

Petunjuk latihan

Gunakan distance = model(time) untuk mengekstrapolasi melampaui data terukur ke time=8 jam.
Cetak distance yang diprediksi lalu periksa apakah nilainya kurang dari atau sama dengan 400.
Jika mobil Anda dapat menempuh paling banyak 400 mil dengan tangki penuh, dan butuh 8 jam untuk berkendara pulang, apakah Anda akan sampai tanpa mengisi ulang? Anda seharusnya memiliki answer=True jika Anda akan sampai, atau answer=False jika Anda akan kehabisan bensin.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Select a time not measured.
time = 8

# Use the model to compute a predicted distance for that time.
distance = model(____)

# Inspect the value of the predicted distance traveled.
print(distance)

# Determine if you will make it without refueling.
answer = (____ <= 400)
print(answer)

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

Latihan Saat Ini

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 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