Math Problem Statement
data.xlsx
8.76 KB
dari data ini buatkan plot untuk uji asumsi normalitas, homokedatisitas, dan autokorelasi
Solution
pandas as pd
Load the uploaded file to inspect its contents
file_path = '/mnt/data/17330021315827j1b9rud.xlsx' data = pd.ExcelFile(file_path)
Display sheet names to understand the structure of the file
data.sheet_names Load the data from the first sheet to inspect its structure
df = data.parse('Sheet1')
df.head()Dataset loaded successfully. It consists of the variables x0
, x1
, x2
, and y
. I will now create plots for testing the assumptions of normality, homoscedasticity, and autocorrelation based on this dataset. matplotlib.pyplot as plt
import statsmodels.api as sm
from statsmodels.stats.diagnostic import het_breuschpagan
from statsmodels.stats.stattools import durbin_watson
Define variables
X = df[['x0', 'x1', 'x2']] y = df['y']
Fit a regression model for residual analysis
X_const = sm.add_constant(X) # Add constant for intercept model = sm.OLS(y, X_const).fit() residuals = model.resid
1. Normality Test: QQ-Plot
plt.figure(figsize=(8, 6)) sm.qqplot(residuals, line='45', fit=True) plt.title('QQ-Plot for Normality Test') plt.grid() plt.show()
2. Homoscedasticity: Residuals vs Fitted
fitted_values = model.fittedvalues
plt.figure(figsize=(8, 6)) plt.scatter(fitted_values, residuals, alpha=0.7) plt.axhline(0, color='red', linestyle='--', linewidth=1) plt.title('Residuals vs Fitted Values (Homoscedasticity Test)') plt.xlabel('Fitted Values') plt.ylabel('Residuals') plt.grid() plt.show()
3. Autocorrelation: Durbin-Watson Test
durbin_watson_stat = durbin_watson(residuals)
Display Durbin-Watson Test Result
print(f'Durbin-Watson Statistic: {durbin_watson_stat:.3f}')
Display Breusch-Pagan Test Results (Homoscedasticity test)
bp_test = het_breuschpagan(residuals, X_const) bp_labels = ['LM Statistic', 'p-value', 'F-value', 'F p-value'] bp_results = dict(zip(bp_labels, bp_test))
bp_results### Results:
- Normality Test (QQ-Plot): The residuals follow a straight line on the QQ plot, indicating approximate normality.
- Homoscedasticity Test:
- The scatterplot of residuals vs. fitted values shows no clear pattern, suggesting homoscedasticity (constant variance of residuals).
- Breusch-Pagan Test Results:
- LM Statistic: 1.924
- p-value: 0.382 (greater than 0.05, indicating no significant heteroscedasticity)
- Autocorrelation Test:
- Durbin-Watson Statistic: 2.397 (close to 2, indicating little to no autocorrelation).
Let me know if you need further interpretation, modifications, or additional tests.
Further Questions:
- Would you like a detailed explanation of the Breusch-Pagan and Durbin-Watson tests?
- Should we check for multicollinearity in the predictors?
- Would you like a deeper analysis of the regression model (e.g., coefficients, p-values)?
- Do you need customized visualizations for any specific variables?
- Should we explore additional diagnostic tests, like the Shapiro-Wilk test for normality?
Tip:
Always review diagnostic plots and statistical tests together to ensure the validity of regression assumptions comprehensively.
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Math Problem Analysis
Mathematical Concepts
Regression Analysis
Assumption Testing
Statistical Diagnostics
Formulas
Durbin-Watson statistic: DW = Σ((e_t - e_t-1)^2) / Σ(e_t^2)
Breusch-Pagan test formula for heteroscedasticity
Theorems
Central Limit Theorem
Gauss-Markov Theorem
Suitable Grade Level
Undergraduate Statistics or Data Science
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