Alasan Melakukan Pemodelan: Interpolasi

Salah satu penggunaan umum pemodelan adalah interpolasi untuk menentukan nilai "di dalam" atau "di antara" titik-titik data yang diukur. Pada latihan ini, Anda akan membuat prediksi nilai variabel dependen distances untuk variabel independen times tertentu yang berada "di antara" dua pengukuran dari perjalanan darat, di mana distances adalah jarak yang ditempuh untuk lama waktu tertentu.

context figure

Latihan ini adalah bagian dari kursus

Pengantar Pemodelan Linear di Python

Petunjuk latihan

Periksa array data yang sudah didefinisikan, times dan distances, serta plot yang sudah dimuat.
Berdasarkan inspeksi awal Anda, perkirakan distance_traveled dari posisi awal pada elapse_time = 2.5 jam.
Simpan jawaban Anda ke distance_traveled.

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Compute the total change in distance and change in time
total_distance = ____[-1] - ____[0]
total_time = ____[-1] - ____[0]

# Estimate the slope of the data from the ratio of the changes
average_speed = total_distance / total_time

# Predict the distance traveled for a time not measured
elapse_time = 2.5
distance_traveled = average_speed * elapse_time
print("The distance traveled is {}".format(distance_traveled))

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

Latihan Saat Ini

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 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