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https://github.com/avinash793/regression-analysis-examples

Detailed implementation of various regression analysis models and concepts on real dataset.
https://github.com/avinash793/regression-analysis-examples

autocorrelation cooks-distance feature-engineering gls-regression-model goodness-of-fit heteroskedasticity influential-cases leverages multicollinearity multiple-linear-regression-model ols-regression-model outliers poisson-regression-model python3 q-q-plot quantile-regression regression-analysis regression-diagnostics residuals simple-linear-regression

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Detailed implementation of various regression analysis models and concepts on real dataset.

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# Regression Analysis Examples



Detailed implementation of various regression analysis models and concepts on real datasets.  



### Regression Models Covered

* Simple Linear Regression Model

* Multiple Linear Regression Model

* Count Based Dataset Regression Models - Poisson, Negative Binomial, Generalised Poisson

* Quantile Regression Model

* Ordinary Least Squares (OLS) Estimate Based Regression Model

* Generalised Least Squares (GLS) Estimate Based Regression Model



### Regression Concepts Covered

You will find implementation of below concepts which can be used for your reference:

* Log Returns

* Ordinary Least Squares (OLS) Estimate

* Generalised Least Squares (GLS) Estimate

* MultiCollinearity

* Variance Inflation Factor (VIF)

* Standardized Residuals

* Studentized Residuals

* Leverages

* Outliers

* Influential Cases

* Cook's Distance

* Regression Diagnostics

* Residual Diagnostics

* Feature Engineering

* Goodness of Fit - Deviance and Pearson Chi-Squared

* Regression Parameters Significant Tests

* Heteroskedasticity

* White's Heteroskedasticity Consistent (HC) Estimator

* Heteroskedasticity & Autocorrelation Consistent (HAC) Estimator

* Q-Q Plot

* LOESS smoothed estimate

* AutoCorrelation

* Simple Linear Regression Model

* Multiple Linear Regression Model

* Poisson Regression Model

* Binomial Regression Model

* Generalised Poisson Regression Model

* Quantile Regression Model



### General Regression Analysis Steps

(It's overall guidance not strict, only for overview)

1. Load Dataset

2. Visualise dataset (if possible)

3. Feature Engineering (if required)

4. Define Regression Model

   * Response variable (y)

   * Explanatory variables or features (X)

   * Residual assumption (start with Gauss Markov Assumption)

5. Feature Selection

   * check for MultiCollinearity and take action

   * Apply PCA 

   

   Goal: features should be independent

6. Fit Regression Model (starts with OLS Estimate)

7. Regression Diagnostics

   * Regression parameters significance using t-test & generalised linear F-Test.

   * Leverages, Outliers and Influential cases

   * R-Squared 

   * For Count based dataset, goodness of fit (Deviance and Pearson Chi-Squared)

   

   Goal: All regression parameters are statistically significant, High R-Squared, 

   model shouldn't be affected by influential cases.

8. Residual Diagnostics

   * Plots:

     * Residual plot only

     * Residual vs fitted values

     * Q-Q plot

     * ACF plot

   * Tests:

     * Homoskedasticity

     * Normal Distribution

     * Auto-Correlation 

   

   Goal: Residual should be white noise.

9. If required delete influential cases, modify model in terms of explanatory 

   variables and | or residual assumption. Go to 6-7-8 step again.

10. Once we have satisfied model, do forecasting + performance metrics on test dataset.