Statistics

Topics covered in Statistics

1. Skewness
1. Introduction to skewness
2. Finding Skewness for different series
• Individual Series
• Discrete Series
• Continuous Series
• Open Ended Intervals
3. Python code for finding skewness
2. Correlation and covariance
1. Need for Correlation
2. Intution behind Correlation
3. Properties of Correlation
4. Inference of Correlation
5. Demerits of Correlation
3. Univariate Linear Regression
1. Regression
2. Comparing our regression model with SciKitLearn and StatsModels
3. Python code for our own Regression model
4. Errors in Regression
4. Multivariate Linear Regression
1. Introduction
2. Gauss Markov Setup and it's assumptions
3. Multivariate Regression equation derivation
4. Proof of Gauss Markov Theorem
5. R² and Adjusted R²
6. Python Code for Multivariate Linear Regression
5. Validating Linear Regression Models
1. Testing significance of regressors
• F Test
• T Test
2. Testing Linearity in the dataset
• Ramsay Reset Test
3. Assumptions of Gauss Markov Setup
4. Assumption of Normality of Residuals
• Jarque Bera Test
• Quantile Qurantile plot
• Kolmogorov Smirnov Test
• Cramer Von Misses Statistic
• Anderson Darling Test
5. Assumption of Homoscedasticity of Resduals
• Breusch Pagan Test
• White Test
6. General inference for the tests
6. Multicollinearity
1. Definition of Multicollinearity
2. Problems with Multicollinearity
3. Steps to detect Multicollinearity
4. Variance Inflation Factor (VIF)
5. Steps for solving Multicollinearity
7. Structural Break
1. Definition of Structural Breal
2. Types of Structural Breaks
3. Methods to detect Structural Breaks
4. Ways to resolve Structural Breaks
8. Gradient Descent
1. Introduction to Gradient Descent
2. Terms related to Gradient Descent
3. Visualizing Gradient Descent
4. Process of Gradient Descent
5. Using Linear Algebra to apply Gradient Descent
6. Python Implementation of Gradient Descent in Linear Regression
9. Neural Netrworks from scratch
1. Introduction to Neural Netrworks
2. Structure of a Neural Netrwork
3. Activation functions
4. Forward Propagation
5. Backward Propagation
6. Updating weights and biases
7. Training a Neural Netrwork
8. Python Implementation of a Neural Netrwork