Complete Linear Regression | Python | Interpretation | Scikit-learn | Statsmodels

Link to colab notebook: https://colab.research.google.com/drive/1zGMm7GiWiycXul7d19qaFWRMWAM7uC56?usp=sharing 1. A systematic approach to creating a random dataset with a known relationship (y = 2x + 5 + noise) 2. Python code using both scikit-learn and statsmodels for the regression analysis 3. Detailed explanation of all output terms including: Coefficients (slope and intercept) Coefficient (slope): This tells us that for each unit increase in X, y increases by approximately 2 units. The coefficient matches our true value of 2 in the data generation process. Intercept: This is the expected value of y when X equals zero. In our case, it's approximately 5, matching our true value of 5. R-squared and adjusted R-squared R-squared (R²): This measures how well the model explains the variation in the data. An R² of 0.976 means our model explains about 97.6% of the variation in y. The remaining 2.4% is due to random noise or other factors not included in our model. Adjusted R-squared: Similar to R², but penalizes adding unnecessary predictors. Since we only have one predictor, these values are very close. F-statistic and its p-value F-statistic: Tests the overall significance of the regression model. A high value (4065) suggests the model is statistically significant. Prob (F-statistic): The p-value associated with the F-statistic. A very small value (1.35e-81) indicates that our model is statistically significant at any reasonable significance level. t-statistics and p-values for individual coefficients & Confidence intervals coef: The estimated coefficient value (slope for x1, intercept for const) std err: Standard error of the coefficient estimates. Smaller values indicate more precise estimates. t: The t-statistic testing whether the coefficient is significantly different from zero. P greater than |t|: The p-value associated with the t-statistic. Small values (less than 0.05) indicate statistically significant coefficients. [0.025 0.975]: The 95% confidence interval for the coefficient. If this interval doesn't contain zero, the coefficient is statistically significant at the 5% level. Diagnostic statistics like Durbin-Watson, Jarque-Bera, etc. Omnibus & Jarque-Bera (JB): Tests for normality of residuals. Non-significant p-values suggest residuals are normally distributed. Durbin-Watson: Tests for autocorrelation in residuals. Values near 2 suggest no autocorrelation. Skew & Kurtosis: Measures of the distribution shape of residuals. Ideally, skew should be close to 0 and kurtosis close to 3 for normal distribution. 4. Residual analysis to verify model assumptions The residual analysis helps us check our model assumptions: The histogram should be roughly bell-shaped (normal distribution) The residuals vs fitted plot should show no pattern (homoscedasticity) The Q-Q plot should follow a straight line (normality of residuals) PS: Ignore background noise 0:00 Introduction 1:25 Importing libraries 2:50 Creating a random dataset 6:30 Visualise dataset 9:45 Running model - Scikit-learn 15:33 Running model - statsmodels 17:28 Visualise result 19:53 Interpretation 31:25 Residual analysis 36:20 Closing notes